Dominance, or domination, is that state which exists when a person or group has power over another. It is the condition or fact of being dominant; the act of exercising controlling power; using or assuming authority.
Social "Dominance hierarchies" are found in many animals species and in humans. In general terms, dominance is having high social status relative to other individuals. Most non-dominants act submissively to dominant individuals.
In individual terms, domination is taking control of a person or situation by any of several means: physical, mental, financial, etc.
Personal dominance is largely about controlling the environment. When that environment includes a partner, a healthy result is a D/s relationship, but that requires that the other partner is submissive and consents to the domination.
In BDSM dominance relationships, the power (or right to make decisions and to give orders) is consensual. The relationship is a mutual one with parties participating in their role, not in the other's. Dominance by coercion or force, without the consent of the people being dominated, is normally called oppression or abuse and is not part of BDSM.
A person who exercises personal power over another in a relationship, or on a regular basis, outside of BDSM scenes, is called a Dominant (also, Dom for a man, Domme or Dominatrix for a woman).
The opposite of dominance is submissiveness.