A person (male or female) who is part of the BDSM subculture, who takes part in a power exchange (partial or total) within a relationship. This doesn't have to be sexual- Dom/sub relationships can entirely exclude sex. The Dom (also known as a Top), takes control over the subs (or bottom) life; this can be in the form of dictating their diet, or what they wear, or more intimate things. The sub often wears a collar to show that they are owned by a Dom.
My Master told me not to drink any alcohol, so I obey him because I am his submissive.