The differential is a mechanical link between the two axes, that enable the driven wheels to rotate independantly from each other.

This is needed for instance when cornering. The outer wheel needs to rotate faster when turning, because it has to travel a longer distance than the inner wheel.

The standard open differential of my C52 gearbox in the background.

Now, I could try to explain the precize workings of a differential. But I'm affraid that will turn into a entire page full of barely understandable text. Pictures don't help here that much either.

A video or a animation would explain more than I could with a whole page of text.

That's why I would like to direct you to the following webpage:

Howstuffworks.

That page should explain how it all works.