The Moon moves around the Earth, taking about one month to complete an orbit. The Moon is "tidally locked" in to position with the Earth such that it always shows us the same side - this is because it takes the same amount of time to rotate on its axis as it does to orbit us around - 27 days.
During its orbit the Moon appears to change shape because only a part of its surface is lit up by the Sun (we only see the Moon because it reflects sunlight). The different shapes are known as Moon Phases and repeat every 29.5 days.
To learn more about the changing phases of the Moon - click here.