The Moon is usually visible for about half of the day -- it's just that most of that time is at night. But occasionally in daylight the Moon can be seen, because it's in the right places for sunlight to hit it and reach Earth at levels high enough for the Moon to be seen above the background sunlight.
The sunlit side of the moon is usually brighter than the sky so in theory is visible during the day if it is in the sky. Because the contrast between it and the day sky is a lot less than with the night sky it is not very noticeable especially as most people rarely look at a clear sky to notice it.