This feast is based on the follow episode recorded in the Protoevangelium of St James:
[When Mary] was two years old, Joachim [her father] said: “Let us take her up to the temple of the Lord, that we may pay the vow that we have vowed, lest perchance the Lord send to us, and our offering be not received.” And Anna [her mother] said: “Let us wait for the third year, in order that the child may not seek for father or mother.” And Joachim said: “So let us wait.”
And the child was three years old, and Joachim said: “Invite the daughters of the Hebrews that are undefiled, and let them take each a lamp, and let them stand with the lamps burning, that the child may not turn back, and her heart be captivated from the temple of the Lord.” And they did so until they went up into the temple of the Lord. And the priest received her, and kissed her, and blessed her, saying: “The Lord has magnified your name in all generations. In you, on the last of the days, the Lord will manifest His redemption to the sons of Israel.” And he set her down upon the third step of the altar, and the Lord God sent grace upon her; and she danced with her feet, and all the house of Israel loved her.
And her parents went down marveling, and praising the Lord God, because the child had not turned back. And Mary was in the temple of the Lord as if she were a dove that dwelt there, and she received food from the hand of an angel.
In his Exposition of the Orthodox Faith, St John of Damascus offers this commentary:
Joachim then took to wife that revered and praiseworthy woman, Anna. But just as the earlier Anna [1 Samuel 1:2], who was barren, bore Samuel by prayer and by promise, so also this Anna by supplication and promise from God bare the Mother of God in order that she might not even in this be behind the matrons of fame. Accordingly it was grace (for this is the interpretation of Anna) that bore the lady: (for she became truly the Lady of all created things in becoming the Mother of the Creator). Further, Joachim was born in the house of the Probatica, and was brought up to the temple. Then planted in the House of God and increased by the Spirit, like a fruitful olive tree, she became the home of every virtue, turning her mind away from every secular and carnal desire, and thus keeping her soul as well as her body virginal, as was meet for her who was to receive God into her bosom: for as He is holy, He finds rest among the holy. Thus, therefore, she strove after holiness, and was declared a holy and wonderful temple fit for the most high God.
The website for the Antiochian Orthodox Christian Archdiocese of North America offers wonderful meditations excerpted from the Byzantine rite. In addition to these, let me commend the collect for the feast from the Western Rite:
O God, who on this day didst vouchsafe that blessed Mary Ever-Virgin, the dwelling-place of the Holy Ghost, should be presented in the Temple : grant, we beseech thee ; that by her intercession we may be found worthy to be presented unto thee in the temple of thy glory. Through Jesus Christ, thy Son, our Lord, who with thee in the unity of the same Holy Ghost, liveth and reigneth God, world without end.