A submissive (abbreviated sub), in a BDSM context, is a person who submits to the will of another person: the dominant. The submissive may or may not receive physical punishment, but the submissive always takes direction and instruction from the dominant.
In consensual spanking, the spankee can assume a submissive role, which may include accepting "punishment" from the dominant. The submissive surrenders control, both mentally and physically. For example, when a spankee is instructed to undress, a submissive follows orders and bares her/his buttocks without question. Thus, he or she willingly surrenders control of the scene.
However note that a spankee is not necessarily submissive, and a spanker is not necessarily dominant. In sensation play, for example, there is no domination and submission. A spankee may also play the role of a recalcitrant brat, or can even be dominant in a scene (see topping from the bottom).
Some people have a more or less fixed orientation as a submissive, while others assume the submissive role for a limited time, perhaps only a single scene. A person who is at some times (or with some people) a submissive, and at other times a dominant, is often called a switch.