It rotates. Just take an orange and a melon (or whatever spherical objects that suits you). Mark a point on the orange with a marker. Now, try to make a circular movement around the melon with the orange, you will see that you can have the mark always face the melon (as the moon is doing with earth) is to have the orange rotate on itself.
Other demonstration: imagine you see the orbit of the moon from the top, it's a circle with Earth in the center. If the Moon always present the same face to Earth, then when it is "up" the circle, this face is down, but when the Moon is "down" the circle, the face is "up". So the Moon rotates.
However, as the Moon rotates almost at the same speed it revolves around Earth, we see "almost" the same face of the Moon, so we think it does move.
However, as the speed is not exactly equals (27.321 66155 day for the revolution, 27.321 661 day for the rotation), we can see a bit more than half the moon, this is called libration. Also, as the orbit of the Moon is elliptic, the speed is not constant, and varies a bit
The phases of the Moon do not come from the rotation of the Moon on itself, but on the revolution of the Moon around Earth (in the picture below, the Sun is "up").
.
