In the episode of the Presentation of Jesus in the temple, St Luke emphasizes Jesus' messianic destiny. The immediate purpose of the Holy Family's journey from Bethlehem to Jerusalem according to the Lucan text was to fulfil the law: "And when the time came for their purification according to the law of Moses, they brought him up to Jerusalem to present him to the Lord (as it is written in the law of the Lord, 'Every male that opens the womb shall be called holy to the Lord'), and to offer a sacrifice according to what is said in the law of the Lord, 'a pair of turtledoves, or two young pigeons'" (Lk 2:22-24).
With this act, Mary and Joseph show their intention of faithfully obeying God's will, rejecting every kind of privilege. Their coming to the temple in Jerusalem has the significance of a consecration to God in the place where he is present.
Obliged by her poverty to offer turtledoves or pigeons, Mary in fact gives the true Lamb who would redeem humanity, thus anticipating what was prefigured in the ritual offerings of the old law.
While the law required the purification after birth of the mother alone, Luke speaks of the "time for their purification" (Lk 2:22), intending perhaps to indicate together the prescriptions involving both the mother and the firstborn Son.
The term "purification" can surprise us, because it is referred to a Mother who had been granted, by a singular grace, to be immaculate from the first moment of her existence, and to a Child who was totally holy. However, it must be remembered that it was not a question of purifying the conscience from some stain of sin, but only of reacquiring ritual purity which, according to the ideas of the time, may be harmed by the simple fact of birth without there being any form of guilt.
The Evangelist uses the occasion to stress the special link existing between Jesus, as "first-born" (Lk 2:7, 23) and God's holiness, as well as to indicate the spirit of humble offering which motivated Mary and Joseph (cf. Lk 2:24). In fact, the "two turtledoves or two young pigeons" (Lk 12:8), was the offering of the poor.
Saint John Paul II, Catechesis on the Creed, December 11, 1996