The Presentation of Jesus in the Temple is described in the Gospel of Luke. According to the Gospel text (Lk 2:22-40), Jesus' parents, Mary and Joseph took the child to the temple to dedicate it to God (Cf. Ex 13:2) on the fortieth day after the birth.

    Purification of Virgin Mary: The feast also celebrates Mary's return to ritual purity after the birth of Jesus, in accord with the proscriptions of the Hebrew Bible.

    After the presentation, the family encountered the old man Simeon, who prayed the Nunc Dimittis and then prophesied about the child. They then met the prophetess Anna, who also praised God because of the child.

    Pope John Paul II has connected the feast day with the renewal of religious vows.

    The law of God, given by Moses to the Jews, ordained that after childbirth a woman should continue for a certain time in a state which that law calls unclean, during which time she was not to appear in public. This term was of forty days following the birth of a son, and double that time for a daughter. When the term expired, the mother was to bring to the Temple a lamb and a young pigeon or turtle-dove, as an offering to God. These being sacrificed to Almighty God by the priest, she was cleansed of the legal impurity and reinstated in her former privileges. A dove was required of all as a sin-offering, whether rich or poor; but as the expense of a lamb might be too great for the poor, these were allowed to substitute for it a second dove. Such was the case, Scripture tells us, for the Holy Family. (Luke 2:24)

    Our Saviour having been conceived by the Holy Ghost, and His Blessed Mother remaining always a spotless virgin, it is evident that She was not subject to the law of purification, but devotion and zeal to honor God by every observance prescribed by His law, prompted Mary to perform this act of religion.

    Besides the law which obliged the mother to purify herself, there was another which required that the first-born son be offered to God, and that after his presentation the child be ransomed with a certain sum of money, and specific sacrifices offered on the occasion. Mary complied exactly with all these ordinances. She obeyed not only in the essential points of the law, but had strict regard to all the circumstances. On the day of Her purification She walked several miles to Jerusalem, with the world’s Redeemer in Her arms. She waited for the priest at the gate of the Temple, made Her offerings of thanksgiving and expiation, and with the most profound humility, adoration and thanksgiving, presented Her divine Son, by the hands of the priest, to His Eternal Father. She then redeemed Him with five shekels, as the law appoints, and received Him back again as a sacred charge committed to Her special care, until the Father would again demand Him for the full accomplishment of man’s redemption.

    The ceremony of this day closed in a third mystery — the meeting in the Temple of the holy prophets Simeon and Anne with the Divine Infant and His parents. Saint Simeon, on that occasion, received into his arms the object of all his desires and sighs, and praised God for the happiness of beholding the much-longed-for Messiah. He foretold to Mary Her martyrdom of sorrow, and that Jesus would bring redemption to those who would accept it on the terms it was offered, but a heavy judgment on all who would obstinately reject it. Mary, hearing this terrible prediction, courageously and sweetly committed all to God’s holy Will. Simeon, having beheld Our Saviour, exclaimed: “Now Thou canst dismiss Thy servant, O Lord, in peace, according to Thy word, because mine eyes have seen Thy salvation.” The aged prophetess Anne, who had served God with great fervor during her long widowhood, also had the happiness of recognizing and adoring the Redeemer of the world. This feast is called Candlemas, because the Church blesses the candles to be borne in the procession of the day, signifying the entry of Jesus as the light of the world.

Jesus Presented in the Temple in Luke:

    ²¹On the eighth day, when it was time to circumcise him, he was named Jesus, the name the angel had given him before he had been conceived.
    ²²When the time of their purification according to the Law of Moses had been completed, Joseph and Mary took him to Jerusalem to present him to the Lord ²³(as it is written in the Law of the Lord, "Every firstborn male is to be consecrated to the Lord" ), ²⁴and to offer a sacrifice in keeping with what is said in the Law of the Lord: "a pair of doves or two young pigeons."
    ²⁵Now there was a man in Jerusalem called Simeon, who was righteous and devout. He was waiting for the consolation of Israel, and the Holy Spirit was upon him. ²⁶It had been revealed to him by the Holy Spirit that he would not die before he had seen the Lord's Christ. ²⁷Moved by the Spirit, he went into the temple courts. When the parents brought in the child Jesus to do for him what the custom of the Law required, ²⁸Simeon took him in his arms and praised God, saying:
    The "Nunc Dimitis": "Now You can dismiss your servant":
    ²⁹"Sovereign Lord, as you have promised,
       you now dismiss your servant in peace.
    ³⁰For my eyes have seen your salvation,
        ³¹which you have prepared in the sight of all people,
    ³²a light for revelation to the Gentiles
       and for glory to your people Israel."
³³The child's father and mother marveled at what was said about him. ³⁴Then Simeon blessed them and said to Mary, his mother: "This child is destined to cause the falling and rising of many in Israel, and to be a sign that will be spoken against, ³⁵so that the thoughts of many hearts will be revealed. And a sword will pierce your own soul too."
    ³⁶There was also a prophetess, Anna, the daughter of Phanuel, of the tribe of Asher. She was very old; she had lived with her husband seven years after her marriage, ³⁷and then was a widow until she was eighty-four. She never left the temple but worshiped night and day, fasting and praying. ³⁸Coming up to them at that very moment, she gave thanks to God and spoke about the child to all who were looking forward to the redemption of Jerusalem.
    ³⁹When Joseph and Mary had done everything required by the Law of the Lord, they returned to Galilee to their own town of Nazareth. ⁴⁰And the child grew and became strong; he was filled with wisdom, and the grace of God was upon him.

http://www.catholic-forum.com/saints/define15.htm
http://en.wikipedia.org/wiki/Presentation_%28Bible%29
http://www.magnificat.ca/cal/engl/02-02.htm
Quotations from NIV at the the bible Gateway