FWD stands for front-wheel drive. The front wheels pull the car about but the rears contribute no propulsion.
AWD stands for all-wheel drive. All four wheels drive the vehicle continuously. A center differential allows operation on ashphalt and other high grip surfaces. More advanced systems have the ability to continuously vary the torque split between front and rear, but both ends are always contributing.
Most AWD vehicles are primarily intended for operation in snow and other low traction environments. Consequently, they frequently lack the low-range transfer case needed for serious off-roading.
But there are exceptions: The Toyota Land Cruiser is AWD, but it has a lockable center differential and a low range transfer case. Unlike many AWD vehicles, it has true off-road capability.
4WD, or four-wheel drive is the classic part-time system that is designed to be operated on normal asphalt roads in two-wheel drive mode and switched-over to 4WD when needed. Depending on the vehicle, either a manual lever or an automatic system is used to make the change. A low-range mode for technical off-roading is nearly always present.
4WD systems generally lack the center differential found in AWD systems, so, when driving on asphalt they must be kept out of 4WD to prevent binding. Of course this doesn't apply during hard-core off-roading, where 4WD, low range and the absence of a center differential are almost always a benefit.