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.