The moon phases
Eight phases of the moon
there are eight phases of the moon their names are: the new moon, the waxing crescent, the first quarter, the waxing gibbous, the full moon, the waning gibbous, the last quarter and the waning crescent. In the northern and southern hemisphere the crescent is facing the opposite direction. Here is a picture.
Why does the moon took different at different times of the month?
The moon looks different at different times of the month because the moon rotates arounds us and we are rotating around the sun. It therefore depends on which how much the light from the sun is reflecting on the moon to determine how much of the moon we see.
Here are examples of how we can see the moon.
If you are still confused here is video to explain it.
The Universe: The Phases of the Moon