Alan P. Boss of the Carnegie Institution of Washington provides an answer to this question:
"The moon keeps the same face pointing towards the Earth because its rate of spin is tidally locked so that it is synchronized with its rate of revolution (the time needed to complete one orbit). In other words, the moon rotates exactly once every time it circles the Earth. The same forces that create tides in the Earth's oceans (from the gravitational pull of the moon and, to a lesser extent, the sun) also act on the solid body of the moon. The Earth's gravitational force on the moon distorts the moon into a slightly oblate or football, shape; In addition, the moon's intrinsic form is somewhat egg-shaped. If the tip of the football/egg does not point toward the Earth, then gravitational forces exert a torque that makes the tip point back toward the Earth. It is very unlikely that the moon started out synchronized; that would indeed be a surprising "coincidence." As Boss explains, "The moon's synchronous spin state is thought to have arisen billions of years ago, when the moon was much closer to the Earth, and so tidal forces were much stronger than at present. The Earth's gravity maintained this spin state even as other gravitational interactions caused the moon to move outward to its present orbital radius.
Q: Why does the moon always present the same face to us?
A: It is pure physics. For starters, the moon is not stuck in place with one side facing us. Our lunar companion rotates while it orbits Earth. It’s just that the amount of time it takes the moon to complete a revolution on its axis is the same it takes to circle our planet — about 27 days. As a result, the same lunar hemisphere always faces Earth.
The moon’s gravity slightly warps our planet’s shape and gives us tides. Likewise, Earth tugs at the moon, creating a rocky, high-tide “bulge” facing us. That bulge ended up working like a brake, slowing the moon’s spin down to the current rate, so the lunar high tide permanently faces us. When that happened, about 4 billion years ago, the moon became “tidally locked,” and it has presented us the same visage ever since.
The lunar cycle/orbit discrepancy:
Although it takes the Moon 29.5 days to complete a lunar cycle, it only takes 27.3 days to complete one orbit of our planet (a sidereal month).
This discrepancy arises from one lunar cycle being defined as the time it takes for the Moon to return to the same phase as seen by an observer on Earth.
Because Earth itself is moving, hurtling through space on its own orbit around the Sun, it takes the Moon that bit longer to catch up than complete an orbit of its own.
You may also wonder why, given the Moon sits in the middle of a line with Earth and the Sun at the point of new Moon, a solar eclipse is such a rare event.
And likewise, why we don’t experience guaranteed lunar eclipses at the time of full Moon. It’s because the Moon’s orbit around Earth is tilted by around 5° with respect to Earth’s orbit around the Sun.
What happens, in most instances, is a near miss.
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