Daytime moon: Why can we sometimes see the moon in broad daylight?

We sometimes see the daytime moon for the same reason we see it at night — it is reflecting light from the sun — and its closeness to Earth makes it brighter than the daytime or nighttime sky. After the sun, the moon is by far the brightest celestial object we can see.
But the daytime moon isn't always visible. This is due to Earth's atmosphere and the orbital cycle of our natural satellite. If our planet didn't have an atmosphere, the moon would be visible from Earth all the time.