January 1 is the next of our twelve days and depending upon which branch of Christendom you are in, the feast associated with this day will change.
In the Catholic church, January 1st is dedicated to the Maternity of the Virgin Mary, a recognition of her carrying the Christ until he was born, and her special role. While not originally celebrated everywhere, it was first made into a festival for the Diocese of Portugal and Portuguese colonies. The image above is a of a famous statue dedicated to the Maternity of the Virgin Mary located in the Basilica of St Augustine in Rome. People have been coming to this statue since it was installed and making prayers and leaving devotions to Mary for aid in having safe deliveries and healthy babies, with people often returning and leaving images of smiling health babies as proof of the holy intercession of Mary.
During Vatican II, the church would formalize January 1 as the Solemnity of Mary and making it official for all Catholics everywhere as her feast day.
In the Orthodox Church, Anglican Communion, and Lutheran churches, January first is dedicated to the Naming of Jesus (and thus his circumcision as well). In the past, a Jewish boy wouldn’t receive his name until he was circumcised, usually eight days after being born. As January 1 is 8 days from Christmas, this would be the time that Jesus would have been circumcised and named, and so other churches recognize this on January 1st instead

What makes this even special is that it is seen as the the first time the blood of Christ was shed, which initiated the beginning of the Jesus’ role as the Savior and with his naming, identifying him as the Son of God. While Jesus was still and infant, the circumcision and his naming marked the beginning of this.
The third aspect of this date is what is called the Octave. While I had talked about this some with the Holy Innocents, January 1, being 8 days from Christmas, is considered the Octave of the Nativity, and thus continues on the Holiness of the birth of Jesus the Christ. The octave of a feast is in one sense considered a continuation of that feast especially Christmas or Easter. While the concept was actually mostly thrown out during Vatican II, the idea persists with some Christians and they recognize it, as it kind of repeats the holiness of the feast. This is tied into certain things within some churches. For one Sunday or the Lord’s day is seen as the Octave as after 8 days, the week always returns to Sunday and thus to Christians as the day of going to church and focusing on Christianity. As it also tied into the circumcision story, and thus the first child baptism, so it is that many baptismal fonts are usually octagonally shaped for that reason.
The use of octaves began under Constantine, and at first was used to celebrate the building of a church. Later the holiest of feasts would be recognized with an Octave day, such as Easter, Pentecost and Christmas, and later certain major saints would received Octave feasts, as a follow up to their initial feast day. In most traditions only one octave was observed, but as the feast of Holy Innocents shows, that day could influence the medieval life for the whole year, and thus the other holy days might also be valued in that way as well, with the day of Christmas being given special recognition for the rest of the new year, and perhaps Pentecost and Epiphany as well.
I had originally encountered this octave in a different way, in relation to candle work. While I had long learned of Novenas which are done for nine days, the Octavo was presented also as an option, which at the time, felt odd to me. When I encountered the Octave here in relation to Christmas and other Christian feasts, I see how it ties in, and how some people would see working for 8 days with candle work or other spells as an effective means as it represents the week coming full circle and in a sense, Ending with the beginning. While a 7 day working would only take up one week, and a 9 day working would exceed beyond it, the 8 day is a kind of equilibrium