What is the difference betwwen "the '80s" and "the 80's"? [duplicate]

"The 80's" is a song made by Robbie Williams - Rudebox.

My question is what is the difference betwwen "the '80s" and "the 80's"? (what does it mean for the different positions of apostrophe?)

the 80's is one of several examples of where apostrophes are or were used within plurals. Some of these are now completely dead in contemporary modern English (e.g. waltz’s was once acceptable because it was a loan word that ended in z, but that would not be acceptable today), and the rest are rather old-fashioned and increasingly not used. It's old-fashioned enough that I would recommend against it. See this answer for more.

'80s is making it clear that the 19 of 1980s has been elided. Generally decade names (80s, 90s, etc.) are easily-enough recognised without it, so this too is not as common as it used to be.

Since they are both forms found, albeit not so often as they once were, you might wonder why '80's is generally not found. As a rule even when apostrophes with plurals were more widely accepted than they are today, one would not use it with a term that already contained an apostrophe. So for example we had the spelling "do's and don'ts" where the first word used the apostrophe with a plural of a mention rather than a use of a word (yet again, not as often done today as in the past) while the last word does not use 's even though it is also a plural of a mention. Similarly, while '80s and 80's are both still found today, and were more common in the past, '80's generally was not.

Strictly speaking, "the 80's" is wrong. Apostrophes are used to denote possession or contraction (as JonHanna points out in the comments, apostrophes have other uses, but these are the only two that we need consider as possibly being relevant here).

The contraction here is from "1980s", so the correct form of the contracted version is '80s. 80s, without the apostrophe, can be seen as a less formal variant of this, but "80's" doesn't really make sense: the only time you would say "the 80's" is if "the 80" (singular) is a thing that can have possessions, and you're referring to one of them.

So, Robbie Williams' song title is grammatically incorrect.