The Moon is constantly traveling around the Earth. It makes a complete orbit of the Earth every 27.3 days.
We only see the part of the Moon reflecting the Sun's light. As the Moon orbits the Earth, the Sun shines on the Moon from different angles. This makes it look like the Moon is changing shape. We call these changes the Phases of the Moon. It actually takes 29.5 days to go from one full moon to the other. This is because the Earth is moving around the Sun, so the Moon has to rotate a little bit more to get back in the same position.
The Moon is "tidally locked" in to position with the Earth. Over millions of years, gravitational forces have slowed down the rotation of the Moon. It now takes the same amount of time to rotate on its axis as it does to orbit us - around 27 days. The result of this synchronous orbit is that the Moon always shows us the same side