An asteroid moon is an asteroid that orbits another asteroid as its natural satellite. It is thought that many asteroids may possess moons, in some cases quite substantial in size. Discoveries of asteroid moons (and binary objects, in general) are very important because the determination of their orbits provides estimates (or at least constraints) on their density and mass allowing an insight into their physical properties, impossible otherwise.

Terminology
As early as 1978, following a stellar occultation, 532 Herculina had been suggested to have a moon and there were reports of other asteroids having companions (usually referred to as satellites) in the following years. A letter in Sky & Telescope magazine at this time pointed to pairs of large craters (e.g. the Clearwater Lakes in Quebec) also suggesting asteroids having companions. However, the first asteroid moon to be confirmed was Dactyl which orbits 243 Ida. It was discovered by the Galileo probe in 1993. The second was discovered around 45 Eugenia in 1998. The first TNO binary, 1998 WW₃₁ was resolved optically in 2002.
As of February 2004, nearly 37 more asteroid moons had been discovered by Earth-bound telescopes. Asteroid moons have been discovered orbiting main belt asteroids, Trojan asteroids, near-Earth objects, and Kuiper Belt objects. In 2005, the asteroid 87 Sylvia was discovered to have two moons, making it the first known triple asteroid. Later the same year, the KBO (136108) 2003 EL₆₁ was also discovered to have two moons, making it the second known KBO to have at least two moons after Pluto.
An example of a double asteroid is 90 Antiope, where two roughly equal-sized components orbit the common centre of gravity. 617 Patroclus and its same-sized companion Menoetius is the only known binary system in the Trojan population.

Discovery milestones
The data about the populations of binary objects are still patchy. In addition to the inevitable observational bias (dependence on the distance from Earth, size, albedo and separation of the components) the frequency appears to be different among different categories of objects. Among asteroids, an estimated 2% would have satellites. Among trans-Neptunian objects (TNO), an estimated 11% are believed to be binary or multiple objects, but three of the four known large TNO (75%) have at least one satellite.
More than 20 binaries are known in each of the main groupings: Near Earth asteroids, Main belt asteroids, and Trans-Neptunians, not including numerous claims based solely on the light curve variation. No binaries have been found so far among Centaurs, presumably due to the much smaller number and relative faintness of these objects.

Common or rare?
The origin of asteroid moons is not currently known with certainty, and a variety of theories exist. A widely accepted theory is that asteroid moons are formed from debris knocked off of the primary asteroid by an impact. Other pairings may be formed when a small object is captured by the gravity of a larger one.
Formation by collision is constrained by the angular momentum of components i.e. by the masses and their separation. Close binaries fit this model (e.g. Pluto/Charon). Distant binaries however, with components of comparable size, are unlikely to have followed this scenario, unless considerable mass has been lost in the event.
The distances of the components for the known binaries vary from a few hundreds of kilometres (243 Ida, 3749 Balam) to more than 3000 km (379 Huenna) for the asteroids. Among TNOs, the known separations vary from 3,000 to 50,000 km.

Origin
What is "typical" for a binary asteroid system tends to depend on its location in the Solar System (presumably because of different modes of origin and lifetimes of such systems in different populations of minor planets).

Among Near-Earth Asteroids, satellites tend to orbit at distances of the order of 3-7 primary radii, and have diameters two to several times smaller than the primary. Since these binaries are all inner-planet crossers, it is thought that tidal stresses that occurred when the parent object passed close to a planet may be responsible for the formation of many of them.
Among main belt asteroids, the satellites are usually much smaller than the primary (a notable exception being 90 Antiope), and orbit around 10 primary radii away. Many of the binary systems here are members of asteroid families, and a good proportion of satellites are expected to be fragments of a parent body whose disruption after an asteroid collision produced both the primary and satellite.
Among Trans-Neptunian Objects, it is common for the two orbiting components to be of comparable size, and for the semi-major axis of their orbits to be much larger − about 100 to 1000 primary radii. A significant proportion of these binaries are expected to be primordial.