This is the subject of scientific debate: there is no universally-accepted explanation. Here are some of the more common theories: The moon broke off from the Earth's crust due to centrifugal force, leaving an ocean basis as a scar, but this would require the Earth to have been spinning too fast. The Condensation or Coformation theory suggests the Moon and Earth formed about the same time from accretion disk of material surrounding the sun. However, there are differences in composition - notably, a lack of iron in the moon - which is hard to explain if they were formed from the same "stuff". Other theories suggest the moon formed elsewhere, and was captured by the Earth's pull, or was formed from a debris field resulting from another cosmic collision. But the currently favored one says the moon was formed from the material thrown out of a semi-molten Earth when something (around the size of Mars!) crashed into it: http://en.wikipedia.org/wiki/Giant_Impact_theory

There have been a number of different theories as to how the Moon formed. However, one of these theories has risen to be the most widely accepted because of discoveries made using the rocks that were brought back from the Moon by the Apollo missions. Trashcity covers the problems with two of these theories pretty well, except for the one that has the Moon forming in a different part of the solar nebula. The problem with that theory is that, if the Moon formed at a different location in the solar system, then it would have a different isotopic composition than Earth. This is not the case. The Moon's isotopic composition is the same as Earth's. Therefore, it formed in our neighborhood. Currently, the most popular model for the Moon's formation is the Giant Impact Model. This model state that as Earth was nearing the end of it's formative period, another planet about the size of Mars crashed into it. This theory explains the observed facts pretty well. When this other planet slammed into us, the debris that was thrown into orbit was superheated. This would have boiled off the volatile elements leaving behind the refractory elements. The iron core of the impactor would have sunk down to join our core. This explains why the Moon is low in iron. The impactor would have formed in our part of the solar nebula. Therefore, it would have the same isotopic composition Earth. So, the debris that this impact threw out would also have the same isotopic composition. Most of the debris generated by this impact would have fallen back to Earth. However, some of it would have had sufficient velocity to go into orbit around Earth. This would have formed a ring of debris that eventually coalesced to form the Moon. Some models indicate that the Moon may have taken as little as one year to form from this debris.

One theory is that the moon was once a small planet complete with its own atmosphere until the disaster that formed the asteroid belt moved it from its orbit and ripped away its atmosphere.