The Moon goes through phases every month, where different amounts of the Moon's surface appear bright. This is because as the Moon orbits the Earth, one side of the Moon is always facing the Sun. As the Moon orbits, we see the Moon in different positions, and in these different positions we see varying amounts of the surface lit by the Sun.
Diagram of the Moon's phases. Credit: Alice Hopkinson, LCO
The lunar phase depends on the Moon's position in orbit around the Earth. This diagram looks down on Earth from north. Earth's rotation and the Moon's orbit are both counter-clockwise here with sunlight coming in from the right. The Moon takes 27 days to orbit the Earth, and the lunar phase cycle lasts about 29.5 days. The lunar cycle takes a little longer because as the Moon is orbiting the Earth, the Earth is also orbiting the Sun, so the Moon needs to travel a bit further round in its orbit to complete a lunar cycle.
New moon happens when the Moon is between the Earth and the Sun, reaching its highest point in the sky in the middle of the day. This means we cannot see the Moon during the night in this phase. As the Moon orbits the Earth, we start to see more of the Moon's lit up surface, until it reaches full moon when it is on the opposite side of the Earth to the Sun. At full moon, the Moon reaches its highest point in the sky in the middle of the night. Past this point, we see less of the lit up surface of the Moon as it orbits back around, until it reaches new moon once more.
We always see the same face of the Moon because it is in a synchronous orbit with Earth. Each time it orbits the Earth it spins once on its axis. As a result, it keeps the same face toward Earth.