Stands for 'Alternate Universe'.

Some games do not accept AU characters.

In role play, AU is occasionally used so that a character can have a relationship with more than one character without technically "cheating".

An alternate universe, as implied, is a universe where things are different from the original.  Maybe only a little, maybe a whole lot.  Maybe instead of humans being the primary race on Earth, your AU says turtles are as smart as humans and humans are as smart as turtles.  Maybe a small puddle turns into a lake of acid.  That kind of thing.