Input torque is applied to the ring gear, which turns the entire carrier (all blue), providing torque to both side gears (red and yellow), which in turn may drive the left and right wheels. If the resistance at both wheels is equal, the planet gear (green) does not rotate, and both wheels turn at the same rate.
History of the Differential
100 BC Antikythera Mechanism (Greek) calculated the position of the stars with over 30 gears
1876 chain-drive differential for use on bicycles (later used in autos by Karl Benz) by James Starley
1897 first use of differential on an Australian steam car by David Shearer
1913 spiral-gear differential by Packard
1926 hypoid differential by Packard
This excellent video shows how a differential works. Produced for Chevrolet by Jam Handy the first 5 minutes of trick motorcycle riding are not directly related but then the narrator really explains the gear functions well.