One very obvious feature of the Moon's spin and orbit around the Earth is that the Moon always has the same side visible from the Earth. Every full moon looks the same. This is somewhat noteworthy because the same is not true of Earth's spin and orbit around the Sun - otherwise, it would be permanently daytime for half the planet, and permanently nighttime for the other half; unpleasant, indeed.
The moon was not always this way. It used to have a spin of its own, so different parts of the surface were visible on successive full moons. The tides (on the Moon!) took away the energy of the Moon's angular momentum so its spin gradually slowed to a halt, the way it is now. The moon is said to be tidally locked to the Earth. Standing on the half of the Moon nearest the Earth, the Earth hovers unmoving in the sky, and standing on the opposite side you'd never see the Earth at all. Since, no matter where you are on the Earth, you will eventually see the Moon in the sky, it is obvious that the Earth is not tidally locked to the Moon - so tidal lock is not necessarily mutual.