Rome is known not only as the See of Peter but as the Apostolic See, because on June 29, 67, not one but two Apostles were martyred there. Saint Peter was crucified upside down near the Vatican hill, and his body was buried under the site of the present-day Basilica of Saint Peter; while, outside the city gates, Saint Paul was beheaded near the site of the present-day Basilica of Saint Paul Outside the Walls, constructed over the Apostle's tomb.
Saints Peter and Paul are traditionally displayed in icons as holding the Church up between the two of them. This is a symbol not only of the importance of the two Apostles but also of the importance of the Apostolic See from the earliest days of the Church--a fact attested to in the early recognition of this feast, which was celebrated by the mid-third century.
In 2008, there is even greater cause for celebration on this feast day. It has been the custom for some years now (since the lifting of the mutual excommunications of East and West in 1965 by Patriarch Athenagoras I and Pope Paul VI) for the Orthodox Ecumenical Patriarch to send delegates to Rome for the Feast of Saints Peter and Paul, while the Pope sends delegates to Constantinople for that Church's great feast, the Feast of Saint Andrew, Apostle (November 30).
In gratitude for Pope Benedict XVI's visit to Constantinople last November, Ecumenical Patriarch Bartholomew I himself made the trip to Rome this year, where he joined Pope Benedict in celebrating vespers the night before the Feast of Saints Peter and Paul and delivered a homily at the papal Mass for the feast. (An Orthodox deacon read the Gospel, and Pope Benedict delivered a homily of his own.)
Even more significant is the fact that Pope Benedict and Patriarch Bartholomew recited the Niceno-Constantinopolitan Creed together during the Mass, affirming the lack of doctrinal difference on any item mentioned in the Creed. (The text was the original text of the Council of Constantinople (381), so it did not include the Filioque clause, which remains a stumbling block to unity, though more for the East than for the West.)
Fr. John Zuhlsdorf at What Does the Prayer Really Say? has posted an audio file of the Patriarch and the Pope reciting the Creed in Greek. It's well worth a listen, especially as encouragement to continue our prayers To Obtain the Reunion of the Christians of the East.