In the Traditional Catholic Liturgical calendar (now often referred to as the ‘Extraordinary Form’) the 1st January is celebrated as ‘The Circumcision of Our Lord and Octave of the Nativity’. It is important not to let the great significance of this feast in the early life of Our Blessed Saviour be overlooked.
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The Circumcision of Our Lord and Octave of the Nativity
In the Liturgy of today three feasts are really included. The first, that which was known in the ancient sacramentaries as “On the octave-day of our Lord”. So the Mass is largely borrowed from those of Christmas.
By the second feast we are reminded that it is to Mary, after almighty God, that we owe our Lord Himself. For this reason, formerly a second Mass was celebrated in the basilica of St. Mary Major, in honour of the Mother of God. Some traces of this Mass remain in the Collect, Secret, and Postcommunion which are the same as in the votive mass of the Blessed Virgin Mary. The psalms at Vespers are also the same as on the feasts of our Lady.
The third feast is the Circumcision which has been kept since the sixth century. Moses commanded that all the young Israelites should undergo this rite on the eighth day after birth (Gospel). It is a type of Baptism by which a man is spiritually circumcised. “See,” says St. Ambrose, “how the whole sequence of the Old Law foreshadowed that which was to come; for circumcision signifies the blotting out of sins. He who is spiritually circumcised by the rooting up of his vices is judged worthy of the Lord’s favour.” While speaking of the first drops of His sacred Blood that our Redeemer shed for the cleansing of our souls, the Church emphasises the thought of the cutting out of all that is evil in us. “Jesus Christ … gave Himself for us that He might redeem us from all iniquity and cleanse us” (Epistle). “O Lord … cleanse us by these heavenly mysteries” (Secret). “May this communion, O Lord, purify us from sin”.
Catholicism Pure & Simple 
Great reminder! Yes, an important aspect of the octave!
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