An automotive drive shaft is responsible for transferring the engine's rotational power, or torque, through the transmission across some distance to one of the car's axles, either from the front of the car to the rear or vice versa. Drive shafts are also responsible for directing power to the wheels.
A car's engine cannot power all of the wheels alone. In a front-wheel drive vehicle, for example, the engine under the hood of the car cannot reach the rear wheels. It is therefore connected under the hood to a transmission, which then must be linked to the car's rear axle via a long drive shaft running the length of the car.
This drive shaft, sometimes known as a propeller shaft, is connected to the final drive of the transmission, sometimes called the differential, located on the rear axle. This rear differential is responsible for redirecting the engine's force 90 degrees each way, to the opposing rear wheels. It also allows the wheels to turn at different speeds. The shafts running from the rear differential to the back wheels are sometimes known as half shafts, but are technically also drive shafts since they drive the turning motion of the wheels.
The drive-train mechanism, which includes the drive shaft, is a complex part of any car. The terms used to refer to its parts vary depending on make, model and mechanic. The basic function of any drive shaft, regardless of its name or location, is to transfer rotational power across distance under the car.