It is a common misconception that Pentecost is the birthday of the Church. The following section from the Pentecostarion translated by Holy Transfiguration Monastery in Brookline, MA speaks of the actual significance of Pentecost and what it means for our ecclesiology.
Such, therefore, are the reasons for today's feast: the coming of the All-holy Spirit into the world, the completion of the Lord Jesus Christ's promise, and the fulfilment of the hope of the sacred disciples, which we celebrate today. This is the final feast of the great mystery and dispensation of God's incarnation. On this last, and great, and saving day of Pentecost, the Apostles of the Saviour, who were unlearned fishermen, made wise now of a sudden by the Holy Spirit, clearly and with divine authority spoke the heavenly doctrines. They became heralds of the truth and teachers of the whole world. On this day they were ordained and began their apostleship, of which the salvation of those three thousand souls in one day was the comely and marvellous first fruit.
Some erroneously hold that Pentecost is the "birthday of the Church." But this is not true, for the teaching of the Holy Fathers is that the Church existed before all other things. In the second vision of The Shepherd of Hermas we read: "Now brethren, a revelation was made unto me in my sleep by a youth of exceeding fair form, who said to me, `Whom thinkest thou the aged woman, from whom thou receivedst the book, to be?' I say, 'The Sibyl.' 'Thou art wrong,' saith he, `she is not.' `Who then is she?' I say. `The Church,' saith he. I said unto him, `Wherefore then is she aged?' 'Because,' saith he, `she was created before all things; therefore is she aged, and for her sake the world was framed."' Saint Gregory the Theologian also speaks of "the Church of Christ ... both before Christ and after Christ" (PG 35:1108-9). Saint Epiphanius of Cyprus writes, "The Catholic Church, which exists from the ages, is revealed most clearly in the incarnate advent of Christ" (PG 42:640). Saint John Damascene observes, "The Holy Catholic Church of God, therefore, is the assembly of the holy Fathers, Patriarchs, Prophets, Apostles, Evangelists, and Martyrs who have been from the very beginning, to whom were added all the nations who believed with one accord" (PG 96, 1357c). According to Saint Gregory the Theologian, "The Prophets established the Church, the Apostles conjoined it, and the Evangelists set it in order" (PG 35, 589 A). The Church existed from the creation of the Angels, for the Angels came into existence before the creation of the world, and they have always been members of the Church. Saint Clement, Bishop of Rome, says in his second epistle to the Corinthians, the Church "was created before the sun and moon"; and a little further on, "The Church existeth not now for the first time, but hath been from the beginning" (II Cor. 14).
That which came to pass at Pentecost, then, was the ordination of the Apostles, the commencement of the apostolic preaching to the nations, and the inauguration of the priesthood of the new Israel. Saint Cyril of Alexandria says that "Our Lord Jesus Christ herein ordained the instructors and teachers of the world and the stewards of His divine Mysteries ... showing together with the dignity of Apostleship, the incomparable glory of the authority given them ...Revealing them to be splendid with the great dignity of the Apostleship and showing them forth as both stewards and priests of the divine altars . . . they became fit to initiate others through the enlightening guidance of the Holy Spirit" (PG 74, 708-712). Saint Gregory Palamas says, "Now, therefore ... the Holy Spirit descended ... showing the Disciples to be supernal luminaries ... and the distributed grace of the Divine Spirit came through the ordination of the Apostles upon their successors" (Homily 24, 10). And Saint Sophronius, Bishop of Jerusalem, writes, "After the visitation of the Comforter, the Apostles became high priests" (PG 87, 3981B). Therefore, together with the baptism of the Holy Spirit which came upon them who were present in the upper chamber, which the Lord had foretold as recorded in the Acts, "ye shall be baptized with the Holy Spirit not many days hence" (Acts 1:5), the Apostles were also appointed and raised to the high priestly rank, according to Saint John Chrysostom (PG 60, 21). On this day commenced the celebration of the Holy Eucharist by which we become "partakers of the Divine Nature" (II Peter 1:4). For before Pentecost,it is said of the Apostles and disciples only that they abode in "prayer and supplication" (Acts 1:14); it is only after the coming of the Holy Spirit that they persevered in the "breaking of bread,"that is, the communion of the Holy Mysteries-"and in prayer" (Acts 2:42).
The feast of holy Pentecost, therefore, determined the beginning of the priesthood of grace, not the beginning of the Church. Henceforth, the Apostles proclaimed the good tidings "in country and town," preaching and baptizing and appointing shepherds, imparting the priesthood to them whom they judged were worthy to minister, as Saint Clement writes in his first Epistle to the Corinthians (I Cor. 42).
All foods are allowed during the week following Pentecost until the beginning of the Apostles Fast the following week.
Apolytikion in the Plagal of the Fourth Tone
Blessed are You, O Christ our God, who made fishermen all-wise, sending upon them the Holy Spirit and, through them, netting the world. O Loving One, glory to You.
Kontakion in the Plagal of the Fourth Tone
When the Most High came down and confounded tongues of men (Babel), He divided the Nations. When He dispensed the Tongues of Fire, He called all to unity, and with one voice we glorify the Most Holy Spirit.