The meeting of Christ by the elder Simeon and the prophetess Anna (Lk 2:22-36) is the main event of the feast of Christ’s presentation in the Temple. It was “revealed to Simeon by the Holy Spirit that he would not see death before he had seen the Lord’s Christ” (Lk 2:26) and, inspired by the same Spirit, he came to the Temple where he met the new-born Messiah, took him in his arms and said the words which are now chanted each evening at the end of the Orthodox Vesper service:
At this time as well Simeon predicted that Jesus would be the “sign which is spoken against” and that he would cause “the fall and the rising of many in Israel.” He also foretold Mary’s sufferings because of her son (Luke 22:34-35). Anna also was present and, giving thanks to God “she spoke of Jesus to all who were looking for the redemption of Jerusalem” (Lk 2:38).
In the service of the feast of the Meeting of the Lord, the fact emphasized is that Christ, the Son and Word of God through whom the world was created, now is held as an infant in Simeon’s hands; this same Son of God, the Giver of the Law, now himself fulfills the Law, carried in arms as a human child.
The Vespers and Matins of the feast of the Meeting of the Lord are filled with hymns on this theme. The Divine Liturgy is celebrated with the lines from the canticle of Mary forming the prokeimenon and the words of Simeon being the verses for the Alleluia. The gospel readings tell of the meeting, while the Old Testament readings at Vespers refer to the Law of the purification in Leviticus, the vision of Isaiah in the Temple of the Thrice-Holy Lord, and the gift of faith to the Egyptians prophesied by Isaiah when the light of the Lord shall be a “revelation to the Gentiles” (Lk 2:32).
The celebration of the Meeting of the Lord in the Church is not merely an historical commemoration. Inspired by the same Holy Spirit as Simeon, and led by the same Spirit into the Church of the Messiah, the members of the Church also can claim their own “meeting” with the Lord, and so also can witness that they too can “depart in peace” since their eyes have seen the salvation of God in the person of his Christ.
It is customary in many churches to bless candles on the feast of the Meeting of the Lord.
(From 'The Orthodox Faith; Volume II - Worship - The Church Year')