Geothermal energy is heat that is contained in the ground and is considered a renewable energy source, much as wind energy is. This means that the heat is merely transferred to and from the ground to condition your home, as opposed to creating heat by expending energy, such as burning natural gas, propane or fuel oil.
Your air conditioner already does this by transferring heat from your house to the outside air, resulting in a cooler house. A heat pump is designed to reverse this cycle in cold weather to transfer the heat from the outside air into your house.
Geothermal systems transfer the heat from deep in the ground instead of the surrounding air. This also has the added advantage of less moving parts, no outside exposure, and lower maintenance.
The simple diagrams below illustrate the heat transfer principles.