Peeling out is when a vehicle exerts more force on the wheels (usually as a result of the driver applying too much throttle) then the friction of the tires and the surface they are on (the road usually) and start to slip. Traction control systems will lower the amount of throttle being applied, where as normal cars will let the tires spin out until the the car starts going fast enough that the tires can start to grip again.
Peeling out is pretty cool and fun to do, but burn outs are more fun.