Why the Moon shows us one face
The Moon never shows us its back. The instinct is that it must not be turning. The truth is the opposite: it turns exactly once per trip around us, and that is what hides the far side.
One face, always
The Moon always keeps the same face turned toward us, and the far side stays hidden from Earth.
The Moon does this because it rotates on its axis in exactly the time it takes to revolve around Earth: about 27.3 days for both. Astronomers call the arrangement synchronous rotation.
Why it matters
Two myths hang on this one fact. The first is that the Moon does not spin. The second is that its far side is a "dark side" that never sees the Sun. Both feel natural and both are wrong. Seeing why separates two motions we normally lump together: going around something and turning on your own axis.
Interactive Drag day through one orbit, then move spins per orbit to 0 or 2 and watch the marked spot swing away from Earth; only 1 holds it there.
Two motions, one period
Revolution is the trip around Earth. Measured against the stars, the Moon completes one every 27.3217 days, the sidereal month. Rotation is the spin about its own axis. Its period is the same 27.3217 days.
Try this with a friend. Stand facing them and walk one full circle around them. If you keep your shoulders fixed toward a distant wall, you will face them, then present your side, your back, your other side, and finally face them again. To keep facing them the whole way round, you must turn your body once per circuit. You did rotate: at the finish you have spun through a full turn. Stick an arrow into a fixed spot on the Moon and it keeps pointing at Earth only because the Moon spins as it goes.
If the Moon did not rotate, the arrow would hold one direction in space while the Moon went round. It would point at Earth once per orbit, and over a month we would see every side of the Moon. We do not.
Now add the Sun. The Moon is a ball in sunlight, so at any moment half of it is lit and half is dark, and which half is lit depends on where the Moon sits in its orbit, not on which side faces us. At full moon the Earth-facing side is lit and the far side is in night. At new moon the far side is lit and the side we see is dark. Because the Moon rotates, the Sun rises and sets on every part of it. The far side is dark no more often than the near side. The nightly change in its appearance is changing sunlight, not a new side turned toward us.
One more number keeps the two cycles straight. The phases repeat every 29.5306 days, the solar month, which is longer than the 27.3217-day orbit. Earth has moved along its own path around the Sun in the meantime, so the Moon must go a little past a full circle to line up with the Sun again.
In short
The Moon spins once for every orbit it makes. A body that did not spin would show us all its sides in a month; one that spins exactly once per orbit shows us one. Sunlight falls on every side in turn, so there is no permanent dark side, only a far side we never see from here.
Where this comes from
- Astronomy 2e, §4.5 Phases and Motions of the Moon linked only, not reproduced
openstax.org/books/astronomy-2e/pages/4-5-phases-and-motions-of-the-moon