geez everybody has a separate explanation.. well here's the right one.
4 wheel drive:
front and rear axle are turned in unison by the transfer case. they ALWAYS turn at the same speed regardless of torque, traction, etc. pros: best traction off road, because power is never taken away from the axle with traction and given to the axle without traction. cons: does not allow for a difference in rotational speeds between from and rear axles. for instance, while turning a corner, one axle (or wheel) is forced to slip due to the difference in distance traveled (the front will make a larger arc around the turn than the rear) so with 4x4 you always have a 2x4 (rear wheel drive usually) option for use on high traction surfaces where this would become a problem (like dry pavement)
AWD (all wheel drive): There is a differential separating the front and rear axles, which allows for a difference in speed between front and rear. AWD is designed for on-road use, giving high performance in low traction conditions (snow, ice, wet roads, dirt roads etc) there is usually a clutch (limited slip) in the center differential, which helps prevent wheel spin on one axle alone. the cons to an AWD system are that it does not perform as well in extreme off-road conditions, it usually cant be disabled (more parts always running) and the biggest con in my opinion is that in most AWD systems, all the tires have to have the exact same diameter or it will damage the center differential. for instance, if one tire is warn down more than the others, you will be forced to buy a whole new set (or risk damaging the system)