A moon is a body in space that orbits another body in space such as a planet or an asteroid. Planets and asteroids are not considered moons because they orbit the sun. Moons are also so-called "natural satellites", meaning they are not man made. We know that satellites like the Hubble Telescope orbit the Earth, but they are not considered moons because they are man-made. There is also a difference between moons and rings. Saturn has several rings (and moons) that orbit it. Rings are made up of dust, ice, and "moonlets", which are small objects that have enough gravity to affect the dust and ice around them, but they are not large enough to be moons. There isn't a rigorous size definition for moons. Astronomers generally just use their best judgement to decide if something is a moon or a moonlet. Astronomers would categorize moons as a body in space that orbits another body that is naturally occurring and that is somewhat large.

There is no official definition (from the International Astronomical Union) for a moon. Some consider any (natural) object which orbits a planet or dwarf planet to be a moon. However, this definition includes any object from a speck of dust to "full-size" moons, so some might try to put a (lower) size limit on moons. Doing so excludes some objects which are readily considered moons (e.g., Mars' Phobos and Deimos.) There is also the problem that if a (potential) moon is very large relative to the parent planet/dwarf planet, then the two could orbit around a center of mass which is not within the (dwarf) planet. This is the case of Pluto and Charon.

A moon is any natural object that orbits a body that isn't a star. The body being orbited can be a planet, dwarf planet, asteroid, comet, or presumably even another moon, although myself I don't know of any moons that have moons of their own. Thus:
-Vesta is not a moon because it orbits a star (Sol), even though Vesta is smaller than many moons in the Sol system.

The International Space Station is not a moon because while it does orbit an object that isn't a star (Earth), it's not a natural object (The U.S. and Soviet space agencies created it).

-Charon is a moon because it is natural, and because it orbits something that is not a star (Pluto), even though Pluto is officially not considered a planet.

A moon is a natural body that orbits around a planet. It's a kind of satellite that formed naturally, not like the satellites we send up to orbit the earth.

A natural satellite is any celestial body in space that orbits around a larger body. Moons are called natural satellites because they orbit planets. Mar 27, 2013
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"The Moon is an astronomical body that orbits Earth as its only natural satellite. It is the fifth-largest satellite in the Solar System, and the largest among planetary satellites relative to the size of the planet that it orbits (its primary)."
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A moon, in astronomy, is something that goes around (orbits) a planet or minor planet. (A minor planet is something that goes around a star, where the star has a system of planets.)