The energy released by fault movement is formed from the motion of the tectonic plates that make up the Earth's crust. As the plates move, they rub against each other and become stuck, where energy is stored until they slip apart and cause an earthquake.
The tectonic plates that comprise the crust of the planet float atop a layer of molten rock, or magma. Convection currents within the magma move the plates. When they become stuck, the energy of their motion builds up along the fault. The plates move slowly but are extremely massive, so they exert tremendous forces on each other. Once the fault breaks free, all of the energy is released in a short amount of time, and the plates often move dramatically.
There are many different types of faults, but all store energy in the same way. One of the most destructive types of faults are found along subduction zones, where one tectonic plate is moving beneath the other. When these faults release their stored energy, they produce what is known as a mega-thrust earthquake. These types of fault ruptures are particularly dangerous when they occur in the ocean, as they can cause massive tsunamis along with powerful earthquakes.