The Moon is not a nighttime-only object. It is often above the horizon during the day, and when that happens you can see it as a pale shape against the blue sky.
NASA explains that the Moon shines by reflected sunlight. At any moment, half of the Moon is lit by the Sun, and the phase you see depends on how the Sun, Earth, and Moon are lined up.
That is why the daytime Moon is easiest to spot in some phases and at some times of day. Around first quarter and last quarter, it often hangs in the sky during daytime hours.
So the reason is not mysterious: the Moon is still there, still lit, and sometimes the daytime sky is dark enough for your eyes to pick it out.
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