Consensus evolved from the meeting process used by, among others, the Religious Society of Friends (Quakers). It is a nonviolent way for people to relate to each other as a group. Consensus allows us to recognize our areas of agreement and to act together without coercing one another. Under consensus, the group takes no action that is not consented to by all members. The fundamental right of consensus is for all persons to be able to express themselves in their own words and of their own will; the fundamental responsibility of consensus is to assure other of their right to speak and to be heard.
Consensus is the name of a broad category of processes - it is not the name of one particular process. The ideals of consensus are not a set of rules, and they encompass more than just decision-making. When we refer to consensus, however, we generally are referring to a set of rules for decision-making that are consistent with the idea and ideals of consensus. Successful use of consensus process depends on people's understanding the idea and wanting to use it.
A detailed outline of the Consensus Model of Decision Making can be found on the Reclaiming website.