Part-time four-wheel drive (4WD) allows a vehicle to be driven in the two-wheel drive mode for ordinary highway and everyday driving (which reduces drivetrain friction and tire wear for improved fuel economy and tire life), and allows it to be switched to four-wheel drive when extra traction is needed (as when driving off-road, on gravel, snow, ice or mud).
Vehicles with part-time four-wheel drive may have manual or automatic locking hubs on the front wheels that must be engaged to change from two-wheel to four-wheel drive. With manual locking hubs, you have to get out of the vehicle and twist a knob on both hubs to engage the front wheels. On some vehicles, the hubs engage and lock when the vehicle is driven backwards momentarily. This saves getting in and out of the car but prevents you from shifting to 4WD on the "fly" (on the go). On other applications, the front hubs do not disengage and turn the front driveshafts at all times.
Vehicles with part-time 4WD also have a "transfer case" that splits drive torque between the front and rear axles. On some vehicles, the vehicle must be stopped or going slower than 2 mph before the transfer case can be shifted from 2WD into 4WD. On others, the transfer case can be shifted on the go regardless of speed.
On Jeeps and similar vehicles, you can also select 4WD low range (4L) or 4WD high range (4H). The low range is for creeping along at slow speeds while driving on rough off-road terrain. The high range is for driving at faster speeds on snow covered pavement or gravel or mud roads.
Full-time four wheel drive, on the other hand, is just what the name implies. All four wheels are constantly driven by the engine to provide maximum traction. This type of setup is used on some performance cars to enhance handling traction. Most such vehicles have a "viscous coupling" in the drivetrain or transfer case that allows a certain amount of "give" in the drive torque between the front and rear wheels. This is necessary to compensate for the different speeds at which the front and rear wheels rotate when turning a tight corner.
NOTE: Four wheel drive does not necessary mean that all four wheels will provide constant drive traction. Unless a vehicle has limited slip differentials, it's possible that either wheel on the front and/or rear axle may lose its grip and spin while its companion just sits there. That's the way standard differentials work. Even so, with four-wheel drive, you will always have at least one front and one rear wheel turning at all times -- which should be enough to pull you through.