Asteroids are a class of small astronomical objects (minor planets, Comets) that orbit the sun. The moons of Mars may have been asteroids that were captured. Those in highly irregular orbits are likely to be the baked rocky cores of comets that have long since lost most if not all of their volatile gasses. In terms of size asteroids range from the biggest 1 Ceres at about 930 kilometers in diameter to objects of a couple hundred tons of mass. Smaller objects are considered Meteorites or Comet Debris.
In terms of Lunar and other space development the main questions boil down to these two: 1)What chance do you or your base stand of getting hit by one? 2)Are the asteroids a better source of water than the moon?
Asteroids and Luna
Categories of Asteroids ranked by semi-axis distance
- Mars Crossing Asteroids
- Main Belt between Mars and Jupiter
- Hilda Asteroids that are close to Jupiter's orbit
- Jovian Trojans 
- Centaurs between Jupiter and Neptune 
Spectral Classification of Asteroids
- C - Carbonaceous 75% of known asteroids (Includes B,D,F,G types)
- S - Silicaceous 17% of known asteroids (Includes A,E,K,L types)
- M - Metallic 8% of known asteroids
Lunar Meteorite Hazard
The current calculated risk of an astronaut on the moon being hit with a micrometeorite is 0.0003 per six hour period (Lunar Base handbook p.526). Assuming the same flux for the Earth and moon then for meteoroids larger than 10 microns in diameter, the rate of impact is 1 per square meter per year. The odds of getting hit by anything bigger assumes you did not pick it up via radar and blast it. The bigger concern involves comets and dusty NEOs that get too close. This could cause a rain of medium velocity particles with a fairly intense flux. As seen with the annual comet swarms, their trails extend for millions of kilometers and vary tremendously in concentration.
Asteroids as potential sources of water
If the Moon appears to have very little water that is accessible, after Earth, the next logical place to get it is the water bearing Asteroids (by spectral analysis). Water is key for sustained development in space for use as rocket fuel and the ability to grow large scale amounts of food. Without it you are always sending expensive things up through the atmosphere of Earth. It takes a lot of water to farm with.
The closest asteroids with a strong spectral signature of water are found about with a perihelion of 2.1 AU. Any closer to the sun or with an axial orientation angled into the sun and the water will have been evaporated from the surface eons ago. There many be water below the surface yet this is a gamble without verification.
Asteroids with near guaranteed water start with 1 Ceres which is the biggest and seems to have had the gravity to hold on to its water. The density calculations for Ceres strongly suggest a rocky core and 60-100km deep ocean with a thin covering of dust & meteorites. Farther out the spectra for water gets stronger and stronger. If an outer main belt asteroid did not form from some major collision, it probably has water. The trick is getting to it and exploiting it.
The major drawback to all asteroid development is the distance involved. Unlike the moon which is close enough where a round trip journey takes a few days, round trip journeys to asteroids take several years using standard rockets. This means that an investor would have to wait years to get a return on their investment, making it economically less attractive than the Moon.
Also, with remotely control robots from Earth, you are looking at delays of 12-30 minutes before a command is received.
Astronauts will have to be in transit for years unless you can afford a very large rocket, or use nuclear propulsion. Although Mars has a deep gravity well, at Mars you can at least count on aerobraking to slow you down. Not so at the asteroids, although the asteroids are most attractive because they have a very shallow gravity well making it easier to recover material from them. Lastly it is very cold on most of these asteroids and that can cause all sorts of problems when the temperature drops to 50 kelvin in the shade.
In short if you can solve the hibernation issues and do without base support for years, the asteroids are a viable source for water.
One possibility is a robotic spacecraft acting as a combination miner and tanker. The only abundant energy source in interplanetary space is sunlight, which points to some form of ion propulsion or solar sail. The probe would sync orbits and dock with a small icy asteroid with negligible surface gravity. Such a maneuver has already been successfully attempted by the Japanese Hayabusa mission. Solar power (either electrical or via reflectors) would be used to heat the asteroid surface, releasing volatiles such as water vapor which would be captured and condensed into storage tanks. A portion of the collected volatiles could then be used as ion thruster reaction mass for the return journey.
Both ion propulsion and solar sailing give continuous but very low thrust, so trips would be long term enterprises lasting decades. The long return times could be made up for in volume; mass production of such water mining craft would amortize the initial design investment and tooling over hundreds of trips.
- McGRAW-HILL ENCYCLOPEDIA OF Science & Technology, 8th Edition, (c)1997 volume 11, page 151.