The major benefit of geothermal energy is that it is a relatively clean source of energy that is essentially limitless.
The two major problems that we face today with our reliance on petroleum are global warming/pollution and the fact that the amount of petroleum that can be extracted is limited. Geothermal does not suffer from either of these problems. It does not emit any greenhouse gasses and it will not run out.
Of course, there are many problems with geothermal energy, the most important of which is the fact that it is only available (given the current state of technology) in a few places in the world.