People often erroneously think that we can see only one side of the Moon because the Moon does not rotate around its axis. But that is not true: we can see only one side of the Moon because it rotates around its axis with the same period as it orbits the Earth. This Demonstration shows the explanation of this phenomenon and, in addition to the real situation, it also shows what would happen if, with the same orbital period around the Earth, the Moon rotated with half or double its period around its axis or if it did not rotate at all.
Suppose that the Moon orbits the Earth above the equator and that the Earth's axial tilt is 0°.
The relative sizes of the Earth and the Moon are to scale but the distance between them is reduced (also the sizes of people are not to scale).
You can change the Moon's rotational period around its axis while its orbital period around the Earth is kept fixed. The value of the Moon's orbital period (which is the same as its rotational period) is 27 days 7 hours 43 minutes (a sidereal month).
The animation shows that if the Moon did not rotate (which is what many people think is the reason we see only one side of the Moon), we could see all "sides" of it.
The rotation of the Earth around its axis, the rotation of the Moon around its axis, and the orbiting of the Moon around the Earth are all counterclockwise looking down to the North Pole. For the setting "double" it can seem that the Moon rotates around its axis clockwise—for that case there is the setting "the Moon only"—use it! If the "illusion" remains, try to turn off the settings "near side of the Moon" and "Earth-Moon line".
The equality of the rotational periods of the Moon and the Earth is due to the tidal forces exerted by the Earth on the Moon. This situation is known as synchronous rotation.