The moderator of the General Assembly is the chairperson of a General Assembly, the highest court of a presbyterian or reformed church. Kirk sessions and presbyteries may also style the chairperson as moderator.
Presbyterian churches are ordered by a presbyterian polity, including a hierarchy of councils or courts of elders, from the local church (kirk) Session through presbyteries (and perhaps synods) to a General Assembly.
The moderator presides over the meeting of the court, much as a convener presides over the meeting of a church committee. The moderator is thus the chairperson, and is understood to be a member of the court acting primus inter pares. The moderator calls and constitutes meetings, presides at them, and closes them in prayer. The moderator has a casting, but not a deliberative vote. During a meeting, the title moderator is used by all other members of the court as a form of address, but this may not be continued outside the meetings. Thus this convention expresses deference to the authority of the court rather than an honour for the moderator as an individual.
Many moderators act as ambassadors for their general assembly when it is not sitting, and visit many of the local churches in their denomination.
In each of the united churches of South India, of North India, of Pakistan and of Bangladesh (which all have Presbyterian roots), one of the diocesan bishops is elected Moderator of the Synod (i.e. the national governing body) for a fixed term -- another is elected Vice-Moderator. The Moderator (for their term) is ranked with the national primates of Anglican churches and styled The Most Reverend.
Lists of moderators of the General Assembly: