Yes it might seem a strange thing to celebrate, but of course the feast day is to mark the importance of the Cathdra that represents the responsibility given to St Peter and his successors including the Bishops to lead the Church. Bishop Paul who seats on the Cathedra in the Cathedral at Lancaster Cathedral which is also called St Peter's. When next visiting the Cathedral try and look for the stained glass window above one of the windows celebrating the life of St Peter. There you will see an image of Lancaster St Peter's and St Peter's in Rome.
A more obvious link is the replica of St Peter's Chair and statue of St Peter which is near the entrance when you come into the Cathedral and has in the past been decorated on its feast day.
For a reflection on today's Gospel and an explanation of why we celebrate this feast why not watch this short video.