You might already know the reason why the moon shines – the moon itself does not have any light, but it reflects the light of the sun and that gives it its shine! The reason why you can see the moon during the day is the same – the sun shines so much light onto the moon that it’s still bright enough to see even in daylight!
Sometimes you might not see the moon during the day, but this usually depends on clouds that are in the way or what phase the moon is in. The moon orbits around the Earth, which is why it sometimes looks like just a sliver and sometimes looks big and full. When it’s in certain phases, the moon can occasionally be harder to spot during the day even though it’s still there!