The Earth rotates in 24 hours. (Actually, a little less, but that's unimportant here.) One side of the Earth is exposed to sunlight at any given time; the other side is in darkness. Thus, we have night and day.
The Moon revolves around the Earth once every 28 days, and is unrelated to the Earth's day/night cycle. If it revolved around the Earth once per day, you'd see the Moon's phase go from full to new and back to full every single day.
One more thing: You can see the Moon during daytime.