First, we've seen this video from the 1930's floating around the Internet quite a bit. It was produced by Chevrolet, but does a really good job explaining how the differential works in your axle. The specifics in modern vehicles are a little different, but the overall mechanical explanation hasn't changed in decades.
As for re-gearing, many people believe that re-gearing a vehicle is for off-road use only, that is not necessarily true. In many cases new gears can be very helpful for everyday driving.
Changing the ratio in your vehicle helps the overall efficiency once your modiciations (wheels, tires, suspension lift) start building up on your vehicle.
Here's quick video that covers the basics of re-gearing. Even thought it's a Jeep channel, the information is still good =)
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