The Dean of Arches is the judge who sits at the Ecclesiastical court of the Archbishop of Canterbury in England.
See here for details of that court's responsibilities. This appeal court is commonly called the Arches Court.
The Dean of Arches is a joint appointment of the Archbishop of Canterbury and the Archbishop of York; he serves the same role in the latter's 'Chancery Court' where he or she has the title of 'Auditor'.