Why is geothermal energy considered a renewable resource?

The heat of the Earth self-replenishes and so is considered renewable.

Geothermal energy refers to energy that is captured from the Earth's crust ( geo referring to Earth and thermal referring to heat). This can be done a few ways:

• the ground, for the first 10 feet or so, is a near constant temperature of 10 C - 16 C degrees. This can be used to cool and heat buildings by using a heat pump,
• hot water from hot springs can be used for heating buildings or heating water,
• steam from hot springs can spin turbines, making electricity

Because the heat of the Earth self-replenishes, it is considered renewable.

http://www.renewableenergyworld.com/geothermal-energy/tech.html