What does 'TL;DR' mean and how is it used?

It means "if you couldn't be bothered to read the preceding material because it looked too long (and possibly boring), here is a summary for you". The meaning is quite close to 'executive summary'.

tl;dr is used to call out another user on the length of their post. However, in cases of more courteous exchanges and serious discussions, tl;dr can be self-invoked by the original poster as a disclaimer to the readers. It is then paired with a brief summary of the longer original text.

KnowYourMeme: tl;dr
urbandictionary: tl;dr

Also useful to know:

Image macros of teal deers are sometimes used in place of tl;dr, due to it sounding close to “tee el dee are.”

The earlier usage ("used to call out a user on the length of their post") has a range of meaning from "please remember, brevity is the soul of wit" to "I find your loquacious verbosity exceptionally tedious. I have ignored your communication in its entirety! Haha!".

This usage can be considered trollish, particularly in the following scenario:

1. I (a troll) ask a seemingly-serious but reasonably complex question, or engage you in what seems to be a serious debate.

2. You respond at some length.

3. I immediately respond "tl;dr!", meaning I am amused that I have induced you to waste your time in composing a lengthy prose argument which is now worthless for want of an audience.

See also: 'Cool Story, Bro!':

A phrase sarcastically used to indicate one's disgust or indifference towards a tl;dr story.

urbandictionary: cool story bro

You might prefer a 'Joseph Ducreux' equivalent - expressing the same sentiment in terms which the writer considers archaic or excessively formal - one of which is:

(I've included the image here because it forms an intrinsic part of the meaning).

An online post which lacks brevity and is not formatted into clear paragraphs or sections could also be criticised as a 'Wall of Text' or 'wall'o'text', "a huge run-on paragraph that makes it difficult to recall the original point". Such a post might justifiably be criticised as being 'tl;dr' - too long (and badly formatted) to read.

It's also sometimes seen (in reference to videos) as 'tl;dw' - "too long; didn't watch".

If you can ignore its hackneyed over-use, then 'tl;dr' can actually be quite a clever riposte, in proportion to the excessive length of the text which it is used to rebut. You can choose to interpret it quite wittily, as "Your views are so marginal, your argument so poor and your writing so unnecessarily verbose that everything you write can be summarily dismissed as beneath my notice; and, in contrast to your rambling statement, I am choosing to demonstrate my intellectual superiority by making this dismissal in a post consisting of only five characters. (This rhetorical strategy is obviously most effective when the replying post consists solely of 'tl;dr').

Attempting to rebut an opponent in an online discussion with 'tl;dr' can backfire. Your thinking opponent will declare that their text is well-written and of appropriate length, and that you would easily have been able to read and understand it, if only your intelligence and literacy were not below par, as (the opponent can argue) is clearly demonstrated by your use of the (to them) ugly neologism 'tl;dr':

Again the image provides vital context for the meaning here: Sir Patrick Stewart's Royal Shakespeare Company training in elocution and his celebrity status, combined with the character Jean-Luc Picard's high status within the fictional world of Star Trek, show the writer attempting to place themselves in a position of intellectual authority; the writer portrays himself as the Captain Picard of usage, dismissing the juvenile prankster's neologism with a well-judged "Shut up, Wesley!".

'tl;dr' can also be used in politics. By projecting it as dialogue into the mouth of one's political opponent, one can imply that they are cavalierly (or through sheer stupidity) ignoring a text which, although it is lengthy and complicated, they should rightly consider extremely important.

Although this particular example happens to feature President Obama, this kind of rhetorical attack is used against people right across the political spectrum, since it's essentially a very general attack on the merit of the political figure as a person, rather than a well-reasoned critique of their policies. In this example the exact same text is being used to attack Sarah Palin.

This technique is particularly effective where the material being ignored relates to the Internet, the very source of the phrase 'tl;dr':

Editorial Cartoon: TL;DR Congress (licensed CC BY-3.0)

In a press release of 28 August 2013, Oxford Dictionaries Online (OUP) included 'TL;DR' on a list of words being added to ODO - interestingly though, it is the one 'new word' on the list in that press release which doesn't have an entry. The definition given in the press release is:

TL;DR, abbrev.: ‘too long didn’t read’: used as a dismissive response to a lengthy online post, or to introduce a summary of a lengthy post.

but the word does not have a proper entry of its own. Even more interestingly, the word seems to have had a definition at ODO, cited here ("early 21st century", click through for more antedating info) as of August 3013, which has now been removed. The OED has bupkis of course.

To clarify the likely intended meaning (in response to a question below):

• if 'tl;dr' is a one-word reply to a lengthy post then it is likely to be intended as a riposte or at best a rebuke to the person who posted the lengthy text, whereas

• if it is placed at the foot of a long post by that post's author together with a summary of that post then it is being used in the 'executive summary' sense, to forestall the possible criticism of excessive verbosity, and

• if it is placed in the mouth of a political opponent then it implies the opponent's cavalier dismissal of (or failure to understand) an important text.

Here on Stack Exchange the 'riposte' or 'putting words in their mouth' meanings would likely fall foul of the SE network's 'be nice' policy. So if you see it here then it almost certainly means 'executive summary'.

tl;dr: Yes.

The "summary" meaning has already been explained, but in a different usage (perhaps the original), it is meant as an insult.

User A: [long impassioned explanation of his views on a particular issue]

User B: tl;dr

Here User B is saying to User A: "Your post was too long and I didn't read it". At best, this is a suggestion that User A is being too verbose and, for the convenience of other readers, should try to summarize his point more concisely. At worst, it suggests that B doesn't believe that anything written by A is worth reading at all, and B is specifically saying this to taunt him with the thought that his epic post is being ignored.

I believe the "summary" meaning grew out of this, as a way of saying: "To forestall those who would tell me tl;dr, here is a brief summary of what I have written."

I have assumed that it now means something like “If you found the above too long and complicated, here is, in a nutshell, what I meant to say.”

Your interpretation as just quoted may be what some writers mean tl;dr to stand for, and is in accord with the explanation from knowyourmeme mentioned in a previous answer. But note that the knowyourmeme entry also says:

Due to its indiscriminate usage by many, tl;dr is frequently considered as spam or meaningless replies by both those unaware of the term and those who are familiar with the meaning.

Because concise, clear, and meaningful phrases¹ are available to use in place of tl;dr, I think there is no reason to use it in ELU answers. Readers who wish to skim an answer, or skip forward to its conclusions, will easily spot those phrases and recognize in a smooth and natural way that they introduce a summary. By contrast, having the words “too long; didn’t read” (or perhaps “too long; don’t read”, or perhaps “WTF?”) appear in one's mind is not a smooth and natural introduction to a summary.

¹ For example, in brief, in short, in summary

Edit: This answer is not intended to say which acronyms are ok and which aren't. Indeed, tl;dr seems ok as a riposte to long, verbose text or as a comment at the end of one's own lengthy text. But as an introduction to a summary, the words behind tl;dr just don't work.

In short, the text where a typical acronym appears still makes sense if words are substituted for the acronym. But that is not true of tl;dr when it is used as a “here is the summary” marker. Writers should avoid so using it.

Your evaluation of what you saw is correct. The "too long; didn't read" abbreviation is now being used to mean, "Too long? Here's a summary". The irony here is that if the post is too long to read, the reader is likely to miss the "tl;dr" part, because it has now been buried in the prose!

It's a symptom of our language being morphed under the weight of the sheer numbers of Web users. In this same fashion, LOL and ROFL have ceased to carry their "out loud" or "on the floor" meanings, and now just mean, "I found this funny" and "I found this really funny".

Sad, what we do to our language, but there it is. It's who we are. But also, see ESR's introduction to the Jargon File, which includes this: "Hackers, as a rule, love wordplay..."