The Moon shows us one face because Earth's gravity slowed its spin.
The Moon turns exactly once for every orbit, so the same side always faces Earth. That is no coincidence: tides raised by Earth's gravity braked its spin long ago. The Moon is doing the same to Earth, slowly lengthening our days, which were once only about six hours long.
Gravity weakens with distance, so Earth pulls harder on the near side of the Moon than on the far side. That stretches the Moon slightly into an egg shape, raising 'tidal bulges'. If the Moon spins faster than it orbits, its rotation drags those bulges ahead of the line to Earth, and Earth's pull on them acts like a brake. Over millions of years this slows the spin until rotation and orbit match. The body is then tidally locked, and it tends to stay that way.
All nineteen known moons in the Solar System big enough to be round are tidally locked to their planets. Pluto and its large moon Charon go further: each is locked to the other, so Charon can be seen from only one hemisphere of Pluto. Most of the Moon's far side remained unseen until the Soviet probe Luna 3 photographed it in 1959. Even so, thanks to wobbles called libration, about 59 per cent of the Moon's surface can be seen from Earth over time.
The braking works both ways. Earth's rotation is being slowed by the Moon, which together with the Sun's tides is thought to have stretched the day from roughly six hours to 24 over about 4.5 billion years. Atomic clocks show the day currently lengthening by about 2.3 milliseconds per century. As Earth slows, the lunar month lengthens too. In principle the two could end up mutually locked, but the Sun is expected to swell into a red giant long before then.
Locking does not always mean one face forever. Mercury, on an eccentric orbit, settled into a 3:2 pattern, spinning three times for every two trips around the Sun. Many exoplanets that orbit close to their stars, such as Proxima Centauri b, are expected to be locked or in similar resonances.
Source: Wikipedia — Tidal locking · Text summarised from Wikipedia (CC BY-SA 4.0)
