How does heat from the earth's core create and destroy the earth?

Heat from the Earth's core creates convection currents in the magma found under the Earth's crust and above the core. These currents constantly move the "tectonic plates" of the crust.

At rifts in the crust (places where two plates are moving apart), the two plates push away from each other, and new rock is formed, which becomes part of the plate and the Earth's crust (creation).

At "subduction zones" (where one plate folds under another), the crust is slowly pushed under the other plate and the weight of it along with gravity pulls it back into the center of the Earth where it melts and becomes magma once again (destruction).

It's a cycle :)