The inside of the Earth is very hot and there is molten rock moving around inside of it all the time.
Thermal Convection
The temperature of the Earth increases with depth. Material is heated at the core and rises up due to it's low density. As it moves up, it spreads out horizontally and makes way for more material to rise. Then it cools and, due to the low density, sinks back to the core. The process repeats over and over EXTREMELY SLOWLY! This could be what drives the plates.
When the material moves up, a divergent plate boundry is formed and the plates spread apart. When the material goes down, a convergent boundry is formed and the plates come back together.
Density
Density is how concentrated the mass (atoms and molecules) in an object or material is. Less dense material rises upward and more dense material sinks. A sponge would float in a pool but a rock wouldn't. Each of the different layers of the Earth has a different density and that's what forms the layers.
