The Feast of Saints Peter and Paul, or the Solemnity of Saints Peter and Paul, is a liturgical feast in honour of the martyrdom in Rome of the apostles Saint Peter and Saint Paul, which is observed on 29 June. The celebration is of ancient origin, the date selected being the anniversary either of their death or of the translation of their relics.
From the Office of Readings for the Solemnity of St Peter & Paul (Apostles)
From a sermon by Saint Augustine
The martyrs had seen what they proclaimed
This day has been consecrated for us by the martyrdom of the blessed apostles Peter and Paul. It is not some obscure martyrs we are talking about. Their sound has gone out into all the earth, and their words to the ends of the world. These martyrs had seen what they proclaimed, they pursued justice by confessing the truth, by dying for the truth.
The blessed Peter, the first of the Apostles, the ardent lover of Christ, who was found worthy to hear, And I say to you, that you are Peter. He himself, you see, had just said, You are the Christ, the Son of the living God. Christ said to him, And I say to you that you are Peter, and upon this rock I will build my Church. Upon this rock I will build the faith you have just confessed. Upon your words, You are the Christ, the Son of the living God, I will build my Church; because you are Peter. Peter comes from petra, meaning a rock. Peter, “Rocky,” from “rock”; not “rock” from “Rocky.” Peter comes from the word for a rock in exactly the same way as the name Christian comes from Christ.
Before his passion the Lord Jesus, as you know, chose those disciples of his whom he called apostles. Among these it was only Peter who almost everywhere was given the privilege of representing the whole Church. It was in the person of the whole Church, which he alone represented, that he was privileged to hear, To you will I give the keys of the kingdom of heaven. After all, it is not just one man that received these keys, but the Church in its unity. So this is the reason for Peter’s acknowledged pre-eminence, that he stood for the Church’s universality and unity, when he was told, To you I am entrusting, what has in fact been entrusted to all. To show you that it is the Church which has received the keys of the kingdom of heaven, listen to what the Lord says in another place to all his apostles: Receive the Holy Spirit; and immediately afterwards, Whose sins you forgive, they will be forgiven them; whose sins you retain, they will be retained.
Quite rightly, too, did the Lord after his resurrection entrust his sheep to Peter to be fed. It is not, you see, that he alone among the disciples was fit to feed the Lord’s sheep; but when Christ speaks to one man, unity is being commended to us. And he first speaks to Peter, because Peter is the first among the apostles. Do not be sad, Apostle. Answer once, answer again, answer a third time. Let confession conquer three times with love, because self-assurance was conquered three times by fear. What you had bound three times must be loosed three times. Loose through love what you had bound through fear. And for all that, the Lord once, and again, and a third time, entrusted his sheep to Peter.
There is one day for the passion of two apostles. But these two also were as one; although they suffered on different days, they were as one. Peter went first, Paul followed. We are celebrating a feast day, consecrated for us by the blood of the apostles. Let us love their faith, their lives, their labours, their sufferings, their confession of faith, their preaching.
Catholicculture.org has more on the feast day HERE.
"Veneration of the two great Apostles, Peter and Paul, has its roots in the very foundations of the Church. They are the solid rock on which the Church is built. They are at the origin of her faith and will forever remain her protectors and her guides. To them Rome owes her true greatness, for it was under God's providential guidance that they were led to make the capital of the Empire, sanctified by their martyrdom, the center of the Christian world whence should radiate the preaching of the Gospel.
St. Peter suffered martyrdom under Nero, in A.D. 66 or 67. He was buried on the hill of the Vatican where recent excavations have revealed his tomb on the very site of the basilica of St. Peter's. St. Paul was beheaded in the via Ostia on the spot where now stands the basilica bearing his name. Down the centuries Christian people in their thousands have gone on pilgrimage to the tombs of these Apostles. In the second and third centuries the Roman Church already stood pre-eminent by reason of her apostolicity, the infallible truth of her teaching and her two great figures, Sts. Peter and Paul."
Phil over at Blue Eyed Ennis has a great post about the day HERE (2013) and last years posts (2012) is available HERE with links, videos and suggested readings about these pillars of the church.
In Rome, the Solemnity is also the day for the imposition of the pallium on the newly appointed archbishops. The pallium is a white scarf made of wool that carries six black crosses, it's meant to symbolize each bishop's unity with the pope. At the beginning of the Mass each pallium is laid over the tomb of St. Peter and then handed to the pope before being presented.
It is traditional for representatives of the other christian churches to attend the patronal feast of the See of Rome particularly the representatives of the Ecumenical Patriarch of Constantinople.