DC decided in the early 80s that they wanted to streamline their "DC universe". Mainly because Marvel outsold them at that point and so they do what companies always do: They imitated their style. Marvel had continuity while DC had just stories. Each issue another one, not much "crossover" between them. And, more importantly, Marvel had "shared universe" they wanted to make us believe that all these characters exist in ONE world while in the DC Universe each character had basically his own "world", heck, you could even say each title existed in a seperate world. Another point where the countless parallel universes (called Earth-1, 2,3, Z, X and whatever). So DC wanted to change all these facts and created a mini-series (not a good story at all, not really a must-read) called "Crisis On Infinite Earths". At the end of this story the "multiverse" collapsed and "merged" into one universe (which was basically Earth-1, although Earth-2 became the "past" of this new reality). BUT despite what people believe the "post-crisis DCU" didn't start back then. The titles were published as if nothing had changed. The multiverse was not longer mentioned, the memories were wiped out. But the guys were basicaly the same ones. Superman continued, Batman continued, Wonder Woman continued. A short time later Superman became the first "post-crisis character" with the mini-series "Man of Steel", his old continuity and adventures were completely erased. So this is the point were post-crisis (for Superman) started. But Batman doesn't have such an event, so people usually associate "Year One" with the start of the new Batman, the point where "post-crisis" starts for "Detective Comics" is debatable, but usually the begin of Denny O'Neil's editorial reign marks the point. Other characters don't have a post-crisis incarnation at all, they stayed the same.
IMO the Crisis was doomed from the start. They didn't streamline continuity, they made it a mess. I mean, what do you expect when you end the storyline with a guy who remembers(!) the old status quo? It didn't affect Batman that much, but Wonder Woman and Superman became new characters.
Timeline:
Crisis (April 1985 - March 1986)
Last pre-crisis Batman story ("Resurrection Night" / "The Night of Thanks But No Thanks", both October 1986)
Last pre-crisis Superman story ("Phantom Zone - The Final Chapter" September 1986)
First post-crisis Batman story ("A Bird in the Hand...", November 1986)
First post-crisis Superman story (""From Out the Green Dawn..."", October 1986)