Usually when you gather for a meeting or gathering there is a Chairman or Chairwoman - the Chair - who guides the meeting, gives order to the procedures, make determinations and often shares wisdom. Where ever they sit is the head of the table, and all eyes and all attention is given to the chair.
In great schools and universities there is usually a Chair that heads the department or branch of study. Often Chairs are established that allow the head of the department to continue study or bring prestige to the discipline. The Chair of the department oversees all aspects of that area of the school or university.
In the normal practice of law, the judge presides from the bench, and the centerpiece of the bench is the position of the judge seated in judgement. Judges do not stand to make their verdicts, they sit on the judges bench or chair. This practice goes back to Roman times.
In the Church, in the local Church or diocese, the bishop's chair (or cathedra) gives name to the primary church of the local church (the cathedral). When he is installed, the bishop is led to the cathedra - the chair - and formally takes possession by sitting and being acknowledged as Shepherd. He is known for his responsibilities to teach, to govern and to sanctify ... all of which are associated with 'the chair".
Today is the Feast of the Chair of Peter, an acknowledgement of the role and primacy of the Bishop of Rome, the successor of Saint Peter. Our gospel today has Jesus asking "Who do you say that I am?" and Peter responding "You are the Christ, the Son of the living God!". Jesus praises the insight of this answer, not because Peter was bright or insightful, but because he was open to be inspired by the Spirit. And Jesus sets him apart - "You are Peter, and upon this "rock" I will build my Church". From that moment on primacy was given to Peter and to his successors. They came to realize that the task of leadership, of teaching, governing and sanctifying, were integral to the office of chief shepherd. And the Chair of Peter - not the literal chair but the office - was to be recognized.
By the mid 4th century, there was a commemoration in Rome of those who had died. This celebration was held between the 13th and 22nd of February, with an "empty chair" placed in their midst. Since the actual date of Peter's death is not known, he was remembered and honored at this Roman remembrance. Today we honor the papacy and with Pope Benedict XVI stepping down next Thursday, the eyes of the world are focused on the Vatican.