Answer: Gravitational force.
Explanation: The force that bounds the Earth and the moon is the gravitational force, and this is why the moon rotates around the Earth.
Now, here the moon is orbiting the Earth is a similar case of how the Earth orbits the Sun and such.
The moon has a given velocity perpendicular to the line that connects it with the Earth, and the gravitational force accelerates the moon in a perpendicular direction with respect to the velocity of the moon, and this is why the moon rotates and does not come towards the Earth.