The moon completes one full rotation about its axis in the same time it takes Earth to complete a full revolution, resulting in one side always turning to face the parent planet in sync with its orbit. This phenomenon is known as tidal locking.
Tidal locking, also known as synchronous rotation, is a common occurrence among astronomical bodies. Besides the Earth-moon system, both moons of Mars and the Galilean satellites of Jupiter are all tidally locked to their primaries.
Tides induced by the larger body in the smaller creates bulges and gravitational distortions, which over millions of years slow an object's rotation down, until it becomes synced with its orbit.