Gravitational potential energy is the energy possessed by masses according to their spatial arrangement and the gravitational force (one of the four fundamental forces) that pulls them towards one another. Since Earth is so large compared to the objects on it, it's easy to watch these objects being pulled (falling) towards the center of the planet, not the planet being pulled towards the object. The direction of Earth's gravitational pull is just called "down."
There's a simulation to play with potential energy that shows the interaction of gravitational potential energy, kinetic energy and spring energy. The simulation below shows how energy flows back and forth between kinetic energy and gravitational potential energy (this is called mechanical energy).
Potential energy due to gravity is calculated using the following formula:
Some forms of hydropower indirectly harness gravitational potential energy. The water behind a hydroelectric dam stores gravitational potential energy since it is at a higher level than the water on the other side of the dam. As the water falls, this potential energy is converted into kinetic energy, which turns turbines to generate electricity.
The University of Colorado has graciously allowed us to use the following Phet simulation. Explore this simulation to see how gravitational potential energy and kinetic energy go back and forth but keep mechanical energy the same. Notice how mechanical energy can be lost and turned into thermal energy, but the total amount of energy still stays the same: