Why did they spell it "URL’s"?
The regular way to pluralize any noun is by adding just an s; the apostrophe should only be added to plural s if the word would otherwise become unreadable or exceedingly ambiguous. A good example would be s's (the plural of the letter s: ss would look like an acronym).
The word URLs would seem to be quite clear: *URL's is probably a simple error made by those confusing it with the possessive 's, which always has an apostrophe (a few pronouns being the exception, like its and hers).
The answer lies in the history of how apostrophes have been used, and how this has then changed:
A Brief, but not that Brief, History of the Apostrophe in English
There’s a myth that the apostrophe is only used for elision. It’s a pretty useful myth, because believing it is unlikely to lead you into mistakes if you are using the most popular styles today, with the possible exception that you might write ones for one’s. (Most other exceptions can be easily absorbed in by considering them, albeit sometimes inaccurately as we’ll see, as a foreign use.)
If though, you want to know why the form URL’s is sometimes still found, then we need to get rid of that notion.
Now, it certainly is true that the apostrophe was first used for elision; that’s what the French invented it for, and that’s what the English borrowed it for. But it was soon put to several other uses.
Some Non-Elision Apostrophes.
Two very early uses were with the anglicisation of Irish and Scottish surnames.
In Anglicising names like Ó Raghallaigh, the English neither wanted to leave the fada in (still not English enough), nor leave the O as a bare word (that would look like an apostrophe in the other sense of the word, directed at someone called Reilly) nor merge them together entirely (which would be too great a change from the original, and hide some possible relationships). Hence they added in an apostrophe to produce O’Reilly. This remains the standard English spelling.
In printing and writing Irish and Scottish (and historically, Manx) names like MacGregor or McGregor, a superscript c was often used: McGregor or MᶜGregor. Some printers substituted a comma turned upside down for this letter*: MʻGregor. Some later printers replaced that with an apostrophe: M’Gregor. This is now rare. One could argue that the letter ʻ was being elided, but the use did not relate to whether the letter was pronounced or not.
The turned comma left a mark in other languages, in that the letter ʻokina used when writing some Polynesian languages in Latin script comes from this too. This is also a case where transcriptions into English can use an apostrophe to replace it; with Hawaiʻi sometimes spelled Hawai’i, and so on.
Note that these are not Gaelic or Polynesian uses borrowed into English; they are English uses as to how words are borrowed, and the O’ example in particular is an anglicisation only ever found in Irish use if someone insists upon the form of their name they use, rather than translating it back (which would be more common).
A final variant of this before we move on to other cases, is the signalling of a glottal stop or syllable separator when transcribing into English. Some languages do use an apostrophe as a letter representing a glottal stop, but there are also cases where English uses it though the language transcribed from does not. The Qur’an and al-Qur’an are fast becoming the most common English spellings of القرآن though there’s clearly no apostrophe in the original; nor in most other transcriptions into European languages. It’s an English thing. Another trancription use is that in mus’haf it signals that the s and h belong to different syllables.
The Genitive Apostrophe comes from Elision, but is not Elision
A case that is only partly elision, is with the genitive. As is well-known, the origin of the apostrophe to produce the genitive originates with the elision of the -es ending that signified the genitive case on nouns.
However, this is not how the modern genitive apostrophe works. It is applied to noun phrases rather than nouns, (“The Prince of Denmark’s tragedy,” not “The Prince’s of Denmark tragedy”) and more significantly, it is used where there is nothing to elide: We have “the gate’s hinges creaked”, though the original genitive of gate would have been gates, not gatees.
So while it originated as an elision, its generalisation to other forms mean it is neither an elided case (since it acts as a clitic on entire noun phrases) nor always an elision (since it’s used where there’s nothing elided). The apostrophe here is acting as much as a separator – signalling that the s is acting upon the word it’s attached to in some special way, rather than a “normal” part of it – as it is an elision.
The Apostrophe as a Separator in Certain Plurals
Compare that with the other cases mentioned so far, and this separator rôle seems to be a reasonable way of understanding its place in O’Reilly, Hawai’i and Qur’an, and even more so in mus’haf.
And it is this role of separator that gives us the use that leads to URL’s.
The most common form of plural in Modern English, is of course the addition of an -s, and all the productive plural forms also end in -s (-es, -ies, -ves). This produces a new word-form and is all very straightforward and normal: Normal English word + Normal English ending = Normal English plural!
There are though several cases that people do, or have, found problematic.
One is with loan words. Let’s say I borrow the word kanelsnegle, because you can’t get decent kanelsnegle in shops here, and I want to point out that mine are the real thing compared to the store-bought rubbish that are either called cinnamon rolls or just lumped under Danishes with several other Danish pastries. Now, if I come to pluralise this, I’ve a few different choices. I can just stick an s on as I would an English word, though that word is neither fish nor fowl. I could use the Danish plural, but many English-speakers wouldn’t realise kanelsnegler was plural. I could italicise just one part of the word to produce “kanelsnegle s”, or I could quote part of it as “kanelsnegle”s.
Once upon a time, one might use an apostrophe here. It was done with loan-words that ended in a vowel, s, z, ch or sh. This use is dead now, but folio’s and waltz’s were indeed once accepted.
Other cases include surnames that ended in -s and perhaps other sibilant sounds (the Jones’s). Another is numbers (the 1900’s), particularly single digits (6’s and 9’s) and single letters (She got A’s in all her exams), particularly when lower case (a’s without the apostrophe is particularly easy to confuse with the word as).
Overlapping with that last case, are mentions of words, rather than uses (If’s and but’s, Do’s and don’ts, this last example also showing a tendency to avoid multiple apostrophes close together†).
And finally, another case is when abbreviations, whether initialisations, contractions, or other forms, are pluralised. Many of our older abbreviations have their own plural, either from doubling (Ss for “Saints”, pp for “pages”, exx for “exemplars”), separate forms, the abbreviation understood to cover both plural and singular cases (NB standing for both “nota bene” and “notate bene”), the abbreviation being inherently plural in all cases (etc.) or uncountable.
The increase in fondness for abbreviations, born of the same impulse to contract that gave us the apostrophe in the first place, introduced many new forms that needed clear and understandable plurals, and so the apostrophe was often put to this use, though some objected that the period (then almost always part of an initialisations and many other abbreviations) already signified an elision and so the s could simply be understood as part of the word that wasn’t elided. So for “Members of Parliament”, one could find M. P.s, M.s P., M.’s P., and M. P.’s according to the author’s preferences.
The Decline and Fall of the Apostrophe
The general move has been toward Shaw’s wish to treat the “uncouth bacilli” with a dose of penicillin, and generally toward less and less use of the apostrophe:
The use for plurals of loan-words is entirely dead, and pretty much everyone would see such a use as incorrect in modern writing. So too are all but one of the more novel genetive pronouns; who’s and it’s‡ completely replaced by whose and its, and are only found in mistakes. While still considered incorrect today, we can conjecture ones might well replace one’s some day, though it does have the possibility of ambiguity.
The use in Irish O’ surnames is pretty much likely to last a long time, with M’ remaining among a few but already pretty rare compared to Mac and Mc forms.
The use as a replacement for the ʻokina is neither fish nor fowl and fails either the consistency of Hawaii nor the faithfulness to the original langauge of Hawaiʻi. It remains not terribly common. It is more reasonable with straight typewriter apostrophes ' which exist for historical reasons and remain a useful shorthand for all of ’, ʻ, ‘, and other similar symbols and letters (useful enough that I’d normally use it here, but that I can’t talk of the difference between ’ and ʻ if I use it).
Almost all the plural forms are dying out. That with abbreviations in particular are now massively less popular than the apostrophe-less alternative, to the point where some people think it’s a mistake comparable to “grocer’s apostrophe’s” rather than an older form. Some still use it when they are using periods in the abbreviation,§ or for lower-case forms but not otherwise, but on the whole it’s dying a quick death.
The use with numbers is dying fast but remains (dropping it gives no risk of ambiguity, and indeed can cause ambiguity with the genitive form as applied to decades). The use with mentions over uses lingers a bit, but is easily replaced with the use of italics. Only that with single letters and digits has much of a current following.
Even the use for elision is rarer now than before, with for example the preterite form of verbs almost never being formed with -’d, only ever with -ed.
The genitive form of most words continues strong, but not in derived names; Companies with genitive names are increasingly dropping them (Waterstone’s becoming Waterstones for example), and apostrophes are disappearing from place names that came from a genitive (there are many places called St. James’ and St. James’s, but expect new places to be St. James while Earl’s Court is only sometimes called Earls Court, the tube station and exhibition centre are both apostrophe-less).
About the only use that the apostrophe is growing in, is in transcriptions, with e.g. Koran being the most common English spelling by far quite recently, and Qu'ran rapidly edging it out.
So in all, we can expect to see fewer URL’s and more URLs as things continue, but we should not be sure to see URL’s linger, and all the more so U.R.L.’s since old habits die hard and this isn’t even that old a habit (I was taught it as the correct form, and I’m not even forty). Though really, who uses URLs for URIs these days, anyway? How often does it really matter to point out that it’s definitely not a URN? How often is it actually the case that it’s definitely not a URN?
* In some fonts, this would also work well for the left single quote, or even a pair for left double quotes, which has left a legacy in that some people still refer to these as “turned commas”, though strictly they are not; turned commas were a printer’s trick of substitution, not the actual symbol the trick was used for. In some fonts (especially larged sized fonts), the trick would not work.
† And increasingly so, Alice sha’n’t do certain things, because Lewis Carroll prefered to be precise, but most of us shan’t. Eliza on the other hand, shant, because George Bernard Shaw argued against most, if not all, uses of the apostrophe, “There is not the faintest reason for persisting in the ugly and silly trick of peppering pages with these uncouth bacilli.” Fo’c’s’le seems to get grandfathered in against this preference from a mix of it colliding so many consonants together, and people remembering its spelling as the one with lots of apostrophes. Even so, fo’c’sle and even foc’sle are both also found. (I note my spell-check complains only of the last).
‡ Its has a long history of battling with both the original his and the logically reasonable it’s (it + genitive ’s), before beating out both to be the genitive third person neuter pronoun, but it’s as a genitive pronoun before around 1800 was a style decision, rather than an error.
§ Itself a practice that is dying out. The period in such cases was originally a mark of elision, and much older in such use than the apostrophe. Most style-guides favour not using them with initialisms, though some will use the form favoured by an organisation that has the initialism as its name, or where it can otherwise be considered authoritative. This still leads to them becoming less common, as said organisations also move to use the period less often. E.g. the B.B.C. became the BBC some time ago. Many do still use them with traditional forms (like I just did with e.g.) and other contractions like op. cit.