The moon rotates around the earth, and the earth rotates around the sun. During the night, when we are on the side of the earth pointing away from the sun, we can see the moon (or the parts of it that are reflecting sunlight in our direction) if it is on the same side of the earth as us. The fact that we can only see part of the sunlit side of the moon is why the moon has phases – new, waxing, full and waning.
During the day, when we are on the side of earth facing the sun, it is still possible (esp. around sunset or sunrise), that the moon is positioned so that we can see part of the sunlit side. But it is much less easy to see, because it’s against the background of the daytime sky (rather than night).
It’s tricky to explain, try drawing yourself some diagrams and see what you can figure out!