I want to add to Jeb Hoge's post, and try to be a little more basic.
Understeer: The car turns less than you are trying to turn it, i.e. the front tire would rather go straight than the direction you are turning them. What causes this? Too much speed while turning, not enough grip/weight on the front tires while turning. Resolution for understeer, decrease speed until sufficient traction returns to front tires.
Oversteer: The car turns more than you are trying to turn it, i.e. the back swings out on you. There are different reasons for why this occurs. The biggest reason is loss of traction with the rear tires due to wheel spin (RWD) or lack of weight on the rear tires. The general response for oversteer is to counter-steer the wheel until the car stops rotating. Alternative responses will depend on the conditions which caused the oversteer.
Hopefully I kept it brief enough.
