A Star is a ball of gas of such a mass that, when compressed by gravity will generate energy due to atomic fusion, and therefore generates light.

A planet is a body that when compressed by gravity will not generate fusion, be it composed of mostly gas or mostly rocky material. It has a stable orbit around a star and also must be of a certain size. Pluto is not a planet mostly due to the fact that is is smaller that our own Moon.

A moon is a rocky celestial body that orbits, mainly, a planet. Big planets may have moons that, if it orbited the star, would be considered a planet.