A moon is a natural body in orbit around a planet, a dwarf planet or an asteroid. They range from worlds larger than Mercury down to captured rocks a few kilometres across, and the giant planets hold nearly all of them. Several are more geologically active than Mars: energy squeezed out of their orbits keeps some of them molten and others liquid under an icy shell, with no help from sunlight at all.
Some formed alongside their planet out of the same disc, which is why the large moons of Jupiter and Saturn orbit neatly in their planet's equatorial plane. Some were captured — passing bodies pulled in, which is why the small outer moons are on tilted, eccentric and often backwards orbits. And at least one, ours, is thought to have been blasted out of the Earth by a collision with a Mars-sized body.
A moon on a slightly non-circular orbit is squeezed harder at one end of it than the other, and that flexing dissipates energy as heat inside the body. It is enough to make Io the most volcanically active object in the Solar System and to keep liquid water oceans under the ice of Europa and Enceladus. Those oceans are the main reason the outer Solar System is searched for life at all.
Seven moons are larger than any dwarf planet, and two of them — Ganymede and Titan — are larger across than the planet Mercury. Size is not mass: both are less than half of Mercury in that, because they are largely ice where it is rock and iron. But several of the large moons have atmospheres, geysers or subsurface oceans, and the argument that a moon is a minor body fails on the first two discs in the row below.
Tides raised on a moon by its planet drag against its rotation and slow it down, until the rotation period matches the orbital period and the same side faces inward permanently. This is tidal locking, and it is the normal fate of a close-in moon rather than a coincidence — most large moons in the Solar System are locked to their planets.