Why does the Moon always show us the same face?
Because the Moon is tidally locked to Earth: it rotates on its axis exactly once for every orbit it completes. The two periods are synchronised, so the same hemisphere always faces us.
A common misconception is that the Moon does not rotate. It does — if it did not, we would see every side of it over the course of a month. The rotation is precisely matched to the orbit, which is a different and much more interesting situation.
How it happened. Earth's gravity is stronger on the near side of the Moon than the far side, and this difference stretches the Moon slightly into an elongated shape — a tidal bulge. Early in its history the Moon rotated faster. As it turned, the bulge was repeatedly dragged out of alignment with Earth, and Earth's gravity pulled back on it, creating a persistent braking torque. Internal friction from this flexing dissipated rotational energy as heat.
Over hundreds of millions of years the rotation slowed until it matched the orbital period, at which point the bulge stayed pointed at Earth and the torque vanished. The system reached equilibrium.
This is extremely common. Most large moons in the solar system are tidally locked to their planets, and Pluto and Charon are locked to each other, each permanently showing the other the same face.
We actually see about 59% of the surface, not 50%, because of libration — apparent wobbles caused by the Moon's elliptical orbit (it speeds up and slows down while rotating steadily), the tilt of its axis, and our shifting viewpoint as Earth rotates.
"Dark side" is a misnomer. The far side receives just as much sunlight; it is simply hidden from us. It was first photographed by Luna 3 in 1959, revealing far fewer of the dark volcanic plains that dominate the near side.
Earth is slowing too, by roughly 1.7 milliseconds per century.