Rear-wheel-drive cars need a rear differential to power the right and left rear wheels and let them turn at different rates of speed when cornering. Front-wheel-drive cars need a front differential for teh same reasons.
Vehicles with full-time or permanenet four-wheel-drive, or with all-wheel drive, require a center differential (or similar device, such as a viscous coupling unit or VCU). In a tight turn, all four wheels travel at different speeds.
A center differential receives power (or more correctly, torque) from the transmission (or transfer box) and sends this torque to the front and rear differentials, while allowing the front and rear wheels to travel at different rates.