This feast commemorates the dedication of the church of Saint Mary which was built in Jerusalem near the site of the Temple. With Christians of the East, the Latin Church also recalls on this day the tradition according to which Mary as a small child was presented to the Lord by her parents in the Temple.
I wasn't completely satisfied with this answer, so I checked the Catechism, Radio Replies, and Catholic Replies. Finally, I decided to just go to the original source, the Protoevangelium of James:
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.There's a reason that the Church didn't include this stuff in the canon of scripture. It might be interesting, but it's not reliable. And yet, the Church recognizes the memorial of the event, and she recognizes Sts. Anne and Joachim as the parents of the Blessed Virgin Mary. I have to assume that some of the content of this particular apocryphal book might be true, but that some of it is not. If I can't tell the difference, and it all sounds a little hokey, I think that it's best for me to stay away from it. I'm going to stick with the canonical books, which contain all of the public revelation necessary for my salvation.