An asteroid is a randomly created celestial body with sizes between 3 and 30 meters.
Currently, asteroids are the only celestial bodies not on rails, meaning that they can be captured by other bodies or interacted with by player controlled space craft. Asteroids can be found and monitored via the tracking station and come in various sizes, ranging from class A (tiny) to class E (Huge). Their coloration ranges from light to dark grey, with patches of black and white dispersed over the surface.
The game counts asteroids as being parts, instead of true celestial bodies. The part configuration file used as a prototype for each procedurally-generated asteroid can be found in GameData/NASAmission/Parts/PotatoRoid/. Because they are parts, asteroids don't have any gravity and do not possess a sphere of influence.
Asteroids should not be confused with captured asteroids, as the latter are on rails and have gravity.
The update in which asteroids were released is called Asteroid Redirect Mission. The general notion is to rendezvous with an asteroid and attach to it with an Advanced Grabbing Unit. The craft can then use its engines to alter the orbit of the asteroid. This can be used to get it into a stable orbit around Kerbin or another celestial body and even land it. Capturing an Asteroid is similar to docking.
The rendezvous is identical to the usual docking with targeting the asteroid and reducing the relative inclination. Although docking or grappling with an escaping target is more difficult, because the instrumentation isn't really implemented to do that sort of docking. On close approach instead of targeting a specific docking port the center of mass needs to be target when the asteroid should be moved. Once grappled it simply behaves as though the ship needs to get a closed orbit and retrograde until it is no longer an escape trajectory.
Depending on the size, exactly hitting the center of mass is not crucial, because the Advanced Grabbing Unit can be tilted to point the thrust better along the center of mass. And when the asteroid is smaller, the unit needs to be gimballed less.
Kerbals which fly close to an asteroid during an EVA can take samples from each asteroid to a maximum of 70 Science. Different samples of equal value can be collected from the same asteroid in different situations, like high orbit, low orbits, atmosphere and even in different biomes when the asteroid is landed on a celestial body.
- Asteroid on Wikipedia