A nice Wikipedia Article
Marvel started noticing early on that in some of their comics, some stories didn't "fit" the timeline or the characters were very different, often due to changing of writers. These timelines just simply weren't canon
So what can you do besides retconning and claiming that everything was canon in the first place?
...well, you could just say they were divergant timelines or alternate universes.
But then how do we know when we're in the "canon" universe and when we're in an alternate universe?
Well, Alan Moore was a genious and decided that we'll just say canon-timelines are on Earth-616 and the rest are... elsewhere. The Exiles number all the Earths, if you're interested.
Now, for some examples. I'm mainly asked about this from X-Men. What is 616-verse and what isn't?
Well, obviously, an early understanding would be all those damn alternate universes. Those are not Earth-616. When we go into the future and see what the future could be like with the control collars et al, that is not 616. Ultimate is not 616.
You might have noticed some small differences...
Age of Apocolypse is not 616. The main storyline, where the characters are in their own time is 616.
So, when asking what 'Verse someone is writing in and they say, oh, comicverse 616, they're saying they're writing in the canon Marvel universe. It's a different phrase in DC comics, but they have the same basic idea.
So, to recap:What is not X-Men 616 Comicverse?
Original Animated X-Men
Age of Apocolypse
Any timeline related to in the comics that isn't
their own. 616 characters may know about these, however!