Phases of the Moon
It takes the Moon around 27 days to orbit around the Earth, during this time we see the Moon go through a series of different shapes, known as the "phases" of the Moon. It takes around 29.5 days for the Moon to get back to exactly the same phase, this is a little longer than it takes it orbit the Earth, due to the fact that the Earth is also moving around the Sun at the same time.
More information on the orbit of the Moon, and why we see these different phases can be found here.
On the animation above you can see the Earth and Moon as seen from above, to the left, where the light from the Sun is coming from the right. On the right panel you can see what the Moon would look like from the surface of the Earth, and a "calendar" showing the days go by. To go to a particular time, move the mouse pointer over the day you want to see.