The moon gives off no light of its own, but merely reflects the sunlight that reaches it. So only half of the moon can be lit up by the sun at any one time.
We on earth can see only that portion of the moon that is lit by the sun. Sometimes the moon, sun, and earth are in such a position that we can see the entire lit half of the moon.
Then the moon looks round, and we have a “full” moon. At other times, we can’t see any of the half of the moon that is lit by the sun. Then we have a “new” moon.
If we can see half of the lit portion of the moon, then the moon looks like a semicircle. If we can see only a quarter of the lit part, then the moon appears crescent shaped. But of course, the moon itself always remains round.