In legal terminology a quorum is the minimum number of members who must be present for a decision-making body (such as a board of directors or a legislative body) to take a vote on a matter. In a database context, a quorum between a principal server, mirror server and a “witness” server allows for automatic failover during database mirroring.
The Microsoft SQL Server TechNet glossary defines quorum as: “in a database mirroring session with a witness server, a relationship in which the servers that can currently communicate with each other arbitrate who owns the role of principal server.”
The witness server as a third party is required to create a quorum. The principal and mirror have one vote each, creating a 1:1 tie and making it impossible to make a decision. A witness allows for the creation of a 2:1 or 1:2 vote, meaning a decision can be made regarding the new principal. An 0:2 vote is also possible if the principal is not available.
Creating a third party witness in effect makes automatic failover possible, because the mirror together with the witness can form a quorum and undertake the decision to failover if contact with the principal is not possible.
Microsoft SQL Server TechNet explains how quorum and automatic failover work: “As long as the current principal server has quorum, this server owns the role of principal and serves the database. If the principal server loses quorum, it stops serving the database. Automatic failover can occur only if the principal database has lost quorum, which guarantees that it is no longer serving the database.”