The dream world lets you do a number of things:
-grow berries -decorate your house -store/trade items with friends -Get pokemon with new abilities (like a blaziken with speed boost) -get pokemon with hold items (like a light ball pikachu)
http://www.serebii.net/blackwhite/dreamworld.shtml
the following link tells you what alternate abilities a pokemon can get.
http://www.serebii.net/blackwhite/dreamworldabilities.shtml
also, note that DW is internet based, not directly in game.
