What causes the moon to appear bright in the sky

It appears white because:

(1) It reflects sunlight, which is white.

(2) It's much brighter than any other object in the sky, so it appears white. If you took a moonrock, brought it back to Earth, and looked at it during the daytime, it would appear grey, but that's only because it doesn't reflect as much light as the objects we would call "white". At night, it's impossible to compare the Moon to "white" objects because there are no white objects illuminated by the Sun.

(3) Not all of the moon is white. If you look at the mares (the dark regions) through a telescope, they're dark gray.

The sun reflects off of an axis and shines back on the moon but the sun is not visible because its on the other side of the world