Pope Benedict XVI
"Cathedra" literally means the established seat of the bishop, located in the mother church of a diocese, which for this reason is called "cathedral," and it is the symbol of the authority of the bishop and, in particular, of his "magisterium," that is, of the evangelical teaching that he, insofar as a successor of the apostles, is called to guard and transmit to the Christian community.
When the bishop takes possession of the local Church that is entrusted to him, he, bearing the miter and the shepherd's crosier, sits on the cathedra. From that seat he will guide, as teacher and shepherd, the journey of the faithful in faith, hope and charity.
Which was, then, the "cathedra" of St. Peter? He, chosen by Christ as "rock" on which to build the Church (cf. Matthew 16:18), began his ministry in Jerusalem, after the ascension of the Lord and Pentecost. The first "seat" of the Church was the Cenacle, and in all probability in that room, where Mary, the Mother of Jesus, also prayed with the disciples, a special place was reserved for Simon Peter.
Pope Benedict on the Feast of the Chair of St. Peter 2-23-06