Luna is Usagi's (Serena) advisor. She is a great black female cat who is committed to Artemis, Mina's white cat, whom she has a daughter with named Diana, Chibi-Usa's little grey kitten.
Luna's first mission was to help Usagi find the Princess of the Moon, while trying to protect the Earth from Queen Beryl's attacks.

After finding that Usagi is in fact the princess of the Moon, together with Artemis, Luna's job is to train the senshi and guide them.

Luna lectures a lot, and detests wasting valuable time on non-essential activities, unlike Usagi. By emitting a moonbeam from her forehead, she can help Usagi and others to remember past memories, and by doing somersaults, she produces the senshi's magical items.

Luna is a deep contrast with the unreliable and lazy Usagi. In the Sailor Moon S Movie, Luna transforms into a human form (Kaguya Hime, Moon Goddess), because she has a little crush on a scientist that is obsessed with the moon. When she transforms, she takes him into the sky flying holding hands (like SuperMan did for Louise) ^^

This is what Luna looks like as a human in the Anime and the Manga:

And this is Luna as the kitty: