* The Moon is incredibly reflective: The moon's surface reflects a significant amount of sunlight, even in the daytime. It's actually much brighter than most objects in the sky.
* The sky isn't uniformly bright: While the sky appears a uniform blue, it's actually darker near the sun and brighter away from it. The moon often appears in a part of the sky that is relatively darker.
* Our eyes are adaptable: Our eyes are capable of adjusting to different light levels. When we look at the bright blue sky, our pupils constrict, but they can still detect the moon's reflected light.
* The moon's phase matters: You're more likely to see the moon during the day when it's closer to being full. A full moon is reflecting the most sunlight.
So, even though the sky is bright, the moon is still reflecting enough sunlight to be visible during the day, especially if the conditions are right.