Originally a constable was a highly ranked staff member of a royal household. The term originally was Old French conestable derived from Late Latin comes stabuli for "officer of the stable". This developed into a term for the chief military officer of an area, castle or army, eg. the Constable of the Tower of London.
The Lord High Constable of England was originally the commander of the royal armies and the Master of the Horse. He would adjudicate in court martials. It eventually became a hereditary position but in modern times is generally inactive except at coronations. Ireland and Scotland have also had a Lord High Constable.
The SCA Constable
The constable makes sure people pay their money at the event and sign indemnity forms, watch out for safety violations, SCA violations, and look after lost property. They are the eyes and ears of the powers-that-be, their mundane security officers (as distinct from any household guards). This person is sometimes called the troll.