What moves the earths plates?

Answer 1

The convection currents in the earth's mantel move the plates.

For more information you can go to these websites:

http://www.windows2universe.org/earth/interior/how_plates_move.html

http://science.nationalgeographic.com/science/earth/the-dynamic-earth/plate-tectonics-article/

Answer 2

The movement of Earth's tectonic plates is primarily driven by the process of mantle convection. Heat from Earth's core causes the mantle to circulate in a convection current, which drags the overlying tectonic plates along with it. This movement leads to the shifting and collision of plates, resulting in the formation of features like mountains, earthquakes, and volcanic activity.