Check out this amazing animation of the moon’s phases over one year put together by NASA and ‘Bad Astronomy’ blogger Phil Plait. Each frame of the animation is one hour of time.
You probably noticed that the Moon appears to rock around, too, tipping and tilting over the course of every month. That’s called libration, and is due to the Moon’s orbit being elliptical, and slightly tilted with respect to the Earth’s equator. We see it from a slightly different angle every day, and that’s what causes that apparent motion.