Someone else will be able explain this better than me, but I'll give it a shot:
"Crisis" refers to a 12-issue series published in 1985-86 called "Crisis on Infinite Earths". The purpose of this series was to take all of the dozens of realites that existed at the point and combine them all into one DC Comics Universe.
Before the Crisis, there were multiple Earths. Earth-2 was where the Golden Age Heroes lived, like the GA Superman, GA Batman, and the JSA (essentially all the DC Comics published from 1938 to the mid-50s). Earth-1 was where the Silver Age heroes lived, like the SA Superman, SA Batman, and JLA (mid-50s to mid-80s comics). Earth-3 was the evil Earth where the JLA members were all villains. Other Earths were "created" when DC would buy up other companies: Earth-S was where Captain Marvel and all the other Fawcett Comics characters lived. Earth-X was where the old Quality Comics charcters lived (and where WW2 never ended, oddly enough). Earth-C was where all the Charlton Comics characters lived (like Blue Bettle and The Question). Lets' see, there was also Earth-Prime, which is sorta of the real Earth where we lived, except there was a Superboy. Earth-C-Minus was where Captain Carrot and the Amazing Zoo Crew lived. Earth-B was where Batman stories that couldn't be fit into the Earth-1 continuity went. There was probably a bunch more Earths, but's it really hard to remember them all.
Anyway, you can see how all this was pretty confusing, which is why they had the "Crisis" and merged all those Earths into one. So now the JSA and JLA and Superman and Batman and Captain Marvel and Blue Beetle and everyone else all exist on the same Earth, and they always have.
As far as Superman goes, they published a mini-series called "Man of Steel" that explained the history of the new, post-Crisis Superman. They were (sort of) starting from scratch, so they could pick and choose which elements of the character's 50-year history to keep, and what to forget about. So, Superman had never been Superboy, cause now he got his powers in his late teens. His parents never died, as they did pre-Crisis. Lex Luthor was now a businessman, not a mad scientist. Lois Lane no longer spent all her time trying to prove that Clark Kent was Superman, cause no one even thought Superman would have another identity. And Superman could no longer toss planets around and use his super-hearing to listen to stuff a zillion miles away; his power level was lessened so that it would still be possible to write stories where he could be threatened.
If you still have more questions, feel free to ask!
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