1. Why do cars even have differentials?

There are no cars that don’t have differentials in them—otherwise we would be driving through tight curves with the wheels spinning and tires screeching. This essential component is located in the center of the drive axle, where its function is to make sure that the two wheels can turn at different speeds when driving around curves, while nonetheless having exactly the same propulsive power. The torque of the motor is always divided in a fixed ratio.
By the way: All-wheel drive vehicles have a differential on each axle, plus a central differential that distributes the engine power between the axles in a given ratio.

2. How exactly does a differential work?

The basic technical principle is usually that of what is called a bevel differential gear, with a differential cage, two planetary gears, and two output shafts. The crucial feature is that the two planetary gears form the connection between the engine’s drive and the two output shafts—but they do this in very different ways:

• When driving straight: The engine drives the differential cage. The planetary gears are stationary at this time. As a result, the cage and the two output shafts all turn at the same speed. This means that the two wheels on the axle also turn at the same speed.
• When driving around curves: Now the outer wheel on an axle has to cover a longer distance, so the two output shafts have to turn at different speeds. To achieve this, the planetary gears in the differential rotate around their own axes at different speeds. This balances out the difference in the speeds of the two wheels.

3. When are differential locks utilized?

The basic technical principle of a differential becomes a problem when the two tires on a driven axle are moving over surfaces that have different traction, such as ice and dry asphalt, for example. The wheel on the ice will spin, while the other will not move at all. The car will be “stuck.” This happens because the differential distributes the drive power of the engine according to the resistance of the tires. The wheel on the ice naturally has significantly less “resistance” so the differential therefore distributes all the drive power to it. Differential locks help to keep things moving in these situations. They redistribute the drive back to the tire that is turning more slowly or not at all. Differential locks come in a number of different types.
A very clear and understandable explanation of the basic principle of a differential is provided by this short film from 1937: