Tegan, a very interesting question. This question was asked some time ago and this is what my team said.
In the 17th Century Newton and another scientist called Hooke did some great observations and experiments on falling objects and proposed that gravity was an attraction between any two masses AND the attraction was dependant on the size of the masses involved.
For example you are attracted by the Earth and the Earth is attracted by you BUT your attraction is so much smaller than that of the Earth it does not affect the motion of the Earth. The attraction between you and the Earth is also dependant upon how far away you are from the Earth. The Moon is attracted by the Earth and the Earth is attracted by the Moon. They are both big bodies so gravity does affect the way they move with respect to each other and this dictates how the Moon orbits the Earth.
Some scientists including Einstein have put forward ideas on how gravity operates but even these are being challenged. There a lots of things which are still unanswered. The questions just have to be asked. Thank you for asking it.
revised 15/01/08 …experiment added.