The moon is orbiting the earth and rotates at a rate such that it turns around exactly once per orbit. This means that the same face is always presented to the Earth.

A similar example is if you get a friend to walk in a circle while always facing the centre, they are rotating once every orbit.

The obvious question is why did this come about, is it just fluke? It is all because of tides; the gravity from the moon distorts the sea (and to a lesser extent the Earth itself) into an ellipsoid. As the Earth rotates this distortion moves around the Earth triggering the tides. The energy to drive the tides comes from the Earth's rotation and the earth is slowing down its rotation - we know that there were 400 days in a year 250 million years ago by studying corals - the Earth also creates tides on the Moon; But because the Earth is about 80 times heavier than the moon they are far stronger. Originally the Moon was spinning, but these immensely strong tides required so much energy that the Moon's rotation slowed down so much it is now always facing the earth. Essentially there are still tides - the moon is distorted, but they are locked in one place, so it is said to be tidally locked.