No concrete evidence explains why there is a moon. The best hypothesis presented is the Giant Impactor hypothesis: It suggests that around 4.45 billion years ago, while the Earth was still forming, a large object hit the Earth at an angle.
How Stuff Works explains the Giant Impactor or Ejected Ring hypothesis: When the large object that was around the size of Mars hit the Earth, it threw debris into space from the Earth's mantle region and overlying crust. After the impact, the object of impact itself melted; and, it merged with the interior of the Earth. The hot debris merged to create the moon.
This hypothesis explains certain things, such as: why the moon has rocks that have a composition similar to the Earth's mantle, why the moon has no iron core, and, why moon rocks look as if they have been baked, although they have no volatile compounds. Computer simulations demonstrate that this hypothesis is possible.
Throughout the years there have been other theories to suggest why there is a moon. Some believe that the moon was made through fission and the Earth moved so rapidly on its axis that a large part of it during the molten stage spun off and formed the moon. Another theory is that the moon and Earth just happened to form at the same time. However, both of these theories have been proven wrong over time.