Gestalt characters have the traits of two classes at once - think of it as multi-classing on steroids.
For example, a 5th level Gestalt Fighter/Wizard (I'll use 3.5 rules because I haven't seen anyone do gestalt in 4E) would have all of the class features of both classes (The Wizard's spellcasting and familiar, and the Fighter's Feats and Base Attack Bonus) but only 5 hit dice.
I've never run or played in a Gestalt game, but the idea is that it gives the players more variety and stronger characters without increasing the power level too much. (A 5th level Gestalt Fighter/Wizard is probably not as powerful as a non Gestalt character that took 5 levels in Fighter and then 5 in Wizard, due to fewer Hit Dice, feats, etc.)