Earth has between 10 and 20 crustal plates, each moving at a different rate. The slowest is the Eurasian plate, which moves less than an inch per year, while the plate with fastest known movement is the Cocos plate, which grinds against the west coast of Central America at an estimated 8.55 inches per year.
The speed with which a plate moves against its neighbors is determined by the rate at which the magma in contact with the plate's underside carries it along. Tectonic plates are not pushed, as the scale of their movement is far too great for their rocks to withstand a lateral force that shoves them along in one direction. Rather, the plates are carried along by currents in the molten parts of the lithosphere that are difficult to detect from the surface.
The engine driving this process is the residual heat of the Earth's interior. This heat drives convection throughout the Earth's mantle and can have unpredictable consequences on the thin crust overtopping it. Near the end of the Mesozoic Era, for example, the landmass that would become India suddenly separated from the southern continent of Gondwanaland and traversed the ocean at nearly 8 inches per year until it crashed into Asia.