Inertia. The moon, the Earth, and everything else in the universe has gravity. The difference is inertia. Think of inertia as constant movement, like a hockey puck sliding across the ice. The puck will go in a straight line until another force acts upon it. Now imagine that you hit that hockey puck so hard that it goes fast enough to achieve orbit around the Earth. What is happening to the puck in this case, is that while the puck is going extremely fast, it is also falling towards the Earth. The thing is that the surface of the Earth is curved, so that the puck falls towards the Earth at a rate equal to the curvature of the Earth. The puck then can never hit the Earth as long as it continues at this speed; as long as its INERTIA remains constant. The same is true for the Moon. The Moon is actually falling towards the Earth, but it is going so fast that the rate at which it falls to the Earth is proportional to the curve of its orbit around the Earth. It is helpful to imagine that everything in the universe is moving, all the time.