A subculture is a group of people with different ideologies and usually fashion and music tastes then that of the larger culture they are a part of. Many subcultures also detest the "mainstream" and commercialization.
Several subcultures flourish because of the almost genetic need for people to belong, most notably youth. Because of this, many corporations have taken notice of them and begun to exploit and profit off said subculture's music or fashion tastes. This leads to a complete bastardization of the original intentions of the group and may kill off the group entirely.
In short, a subculture is a group detaching itself from "mainstream" society, catering to certain people's ideologies and preferences.
The punk movement is an excellent example of the rise and fall of a subculture.