Data from the lunar surface has offered hints that the moon may have frozen water at the poles, but we now have real evidence, gleaned from the Moon Mineralogy Mapper (MMM) that NASA placed on the Indian Chandrayaan-1 spacecraft, which went into orbit around the moon in 2008. The water ice is in holes, called "cold traps," at both poles, and in some places accounts for 30% of the material analyzed.
That's pretty amazing. It's really weird to think that the moon, with no air and nothing to protect the surface from the blazing Sun, can have ice, let alone ice on the surface! But they do have protection: the Moon itself.
Near the poles, the Sun is always low to the horizon. If you get a deep crater, say, then there can be spots along the floor that the Sun never gets high enough to shine on. They are perpetually dark, and very cold. We know comets and asteroids can contain quite a bit of water, and that can be released as a vapor when they impact the Moon. If there's an impact near a deep polar crater, some of that water may settle there. On the surface exposed to sunlight the water won't freeze, and will eventually get broken up by ultraviolet light. But if it gets into a cold trap, well, it's trapped by the cold.