The feast of the Chair of St Peter has been celebrated since very early in Church history. It is a feast to celebrate the unity of the Church.
Jesus chose from among his disciples twelve whom he made apostles. From among this group he chose one to head the new Church. Jesus first put in place the authority and left the rest of the founding of his church to time and experience. But the authority has been there from the beginning.
In the Creed we say, "I believe in One holy Catholic and Apostolic Church."
The Church is One with one visible head. The unity of the Church is paramount because Jesus is One and the Church is the Mystical Body of Jesus on Earth.
As Catholics we believe that the Church herself is a mystery in that she is the visible presence of Jesus in the world today.
This is the starting point for understanding the Church and all she does. The communion of the faithful throughout the world, taken as a group and under the influence of the Holy Spirit form part of the Mystical Body of Christ.
While Jesus is the head of the Mystical Body in heaven, the Pope, the successor of St Peter, who now occupies the Chair of St Peter, is the visible sign of that body on earth.
What a wonderful Church we belong to: we have a direct line to Jesus as head in heaven! Wow!