Why cars need a differential
When a car turns, its two driven wheels travel different distances. The differential splits engine power between them while letting them spin at different speeds.
Power comes in
The driveshaft spins the small pinion gear, which drives the big ring gear. This turns the motion 90 degrees toward the wheels and multiplies torque.
The carrier
The ring gear is bolted to the carrier, so the whole carrier spins with it, taking the cross pin and spider gears around the axle line.
Spider and side gears
The spider gears mesh with a side gear on each axle. As the carrier turns, the spider gears push both side gears, and so both wheels, around.
Driving straight
On a straight road both wheels resist equally. The spider gears do not rotate on their pin; they act like a solid block and both wheels turn at the carrier's speed.
Taking a turn
In a turn the outer wheel must cover the longer path. The spider gears now roll on their pin, so the outer wheel speeds up exactly as much as the inner one slows down; the average always equals the carrier speed.