There are two terms generally used, namely, rotation and revolution. The rotation means spinning on its own axis, just like a spinning top. The revolution means moving around another object in an orbit.

Answering to the above question, we can say, moon revolves around the earth once in every 27.332 days.  It also takes approximately 27 days for the moon to rotate once on its axis. As a result, the moon does not seem to rotate about its own axis.

Moon is the only permanent natural satellite of earth. Hence, moon revolves around the earth.

There is a gravitational force between the Moon and the Earth. This tries to pull the Moon toward the earth. This constant pull on the Moon as it moves around the Earth is called a "centripetal" force. This force is balanced by the "centrifugal" force,  that pulls on the Earth and keeps the moon in motion. It is the balance between the centripetal and centrifugal forces that keep the Moon in orbit around the Earth.