AverageBear: Reversion means when you 'undo' a turn - basically if you think you have made a wrong choice you can go back one turn!
It allows you to recover from serious errors like when your main hero + army get wiped out in a fight or some really bad random event happens. Of course, if you go back a turn beneficial random events that happened on this turn may also not occur...
It reduces your final score so try not to do this too much...
regnak: Thanks.
A few things to add to this. First, it's possible to go back more than one turn, by doing multiple reversions in a row. That'll hurt your score significantly, of course, and isn't an idea I've ever used.
Secondly, it seems that the same random seed is used when you reverse. That means that (with the possible exception of if you do something requiring the random number generator before clicking 'end turn'), you'll get the same random events. That will, however, allow you to prepare by, say, moving a hero into the province that you know will be attacked by harpies to defend it. You can also choose different options if you got a terrible result.