In basic terms a mechanical differential is a gearing system, its purpose is to allow wheels mounted on the same axle to rotate independently of each other. In really simple motoring journalism terms a mechanical differential allows you to go sideways. However, the differential is an ancient device that was first invented by the Greeks of Alexandria in the third century BC. The Greeks used a differential based gearing system to create what is considered to be the worlds first computer, the Antikythera device.
The ancient world used differentials to power heavy machinery, irrigation wheels, and mills. Lets fast forward a few millennia. The modern automotive differential was invented in 1827 by a Frenchman, Onésiphore Pecqueur.
Of course over the years the automotive differential has evolved in terms of complexity and usage. Indeed there are no less than 8 different types of mechanical differentials used in the automotive industry.
Engineering Explained YouTube man does his best teenage Justin Bieber impersonation as he talks differentials. (how old is this guy?)