I mentioned in my sermon on Christmas Day that the readings in this season would show us how deeply our Lord entered into humanity, except for sin, which He nevertheless took upon Himself to redeem us.
The readings in the traditional Latin Mass missal are very doctrinal. So what we see in the readings today is that our Lord entered into the Old Testament law. He is presented in the temple now, for Mary and Joseph to make the required offering for His birth. But already we see the portent of what is to come. Simeon and Anna appear, moved by the Spirit. The Old Testament law was in preparation for the Messiah, and now our Lord has come, and He fulfills the law. He will send the Holy Ghost to remind the Church of everything He said, and to show us the way to live our faith.