What is a ghost on Super Mario Galaxy 2?

Answer 1

You mean a green ghost? Well, after you beat a level with Luigi, a green ghost will appear in that level. if you go to that level you'll find a little ghost of Luigi. Press A or spin near it and it will start running to the end of the course. You can race it if you want, but don't need to.

Answer 2

Go back to the level, and you should see a luigi near the start off the level running in place and when you touch him, he will sometimes show you stuff like hidden coins, the comet medal, etc, or he will race you to the end of the level and hang on to the star, which is funny the first time you see IT.