Look up on a clear night and you see the same dark patches, the same "face", as people did thousands of years ago. Nobody ever saw the other side until a Soviet probe, Luna 3, photographed it in 1959. Is the Moon not spinning? It is. It spins exactly once every time it goes around the Earth, and that is no coincidence.
The Moon takes about 27.3 days to circle the Earth, and about 27.3 days to turn once on its axis. Walk in a circle around a chair while always facing it: the chair sees only your front, yet you have turned a full 360 degrees by the time you get back. The Moon does the same thing.
Try it below. The Moon orbits the Earth; the lime flag marks one spot on its surface and the grey flag the opposite spot. Drag the slider to change how many times it spins per orbit. The small disc on the right shows what the Moon looks like from Earth.
The Earth's gravity pulls harder on the near side of the Moon than on the far side. That stretches the Moon slightly into a lemon shape with the long axis pointing at Earth. If the Moon spins, its rock is dragged around that bulge and flexed, again and again, and the friction turns spin energy into heat.
Gravity also pulls on the bulge itself. When the long axis is off the Earth line, Earth's pull twists it back, like a compass needle. Press the last button above: the Moon starts spinning fast, and the twist plus friction slow it until the bulge points at Earth for good. The tides can only finish their work when the spin matches the orbit, so that is where the spin ends up. (The simulation is a cartoon with made-up strength and speed; the real process took far longer, likely millions of years.)
The same thing happens elsewhere. Pluto and its moon Charon are locked to each other, so each shows the other only one face. Many large moons of the giant planets, including Jupiter's four big moons, also keep one face toward their planet. Mercury, which you may have met in an earlier break, is locked a different way, spinning three times for every two orbits.
If you watch the Moon for years, you can see about 59 percent of its surface over time. The Moon's orbit is slightly oval, so it moves faster when near Earth and slower when far, while its spin stays steady. The spin runs a little ahead, then a little behind, so the face seems to nod and sway a few degrees. Astronomers call this libration. Set the slider near 1 but not exactly 1 and you can watch the face slowly drift, the same effect on a larger scale.
Tides work both ways. The Moon raises tides in Earth's oceans, and Earth's spin drags those bulges slightly ahead of the Moon, pulling it forward. That speeds the Moon along and lifts it into a wider orbit. Laser reflectors left by the Apollo astronauts show it moving away at about 3.8 centimetres a year, roughly the speed your fingernails grow. In the other direction, Earth's day gets longer by a tiny amount each century.