Before the re-hashing of the Liturgy, the Epiphany of the Lord was celebrated in the Church on 6th January. In many countries, and among most traditional Catholic orders (the twelfth day after the feast of the Nativity) the feast of the Epiphany continues to be kept on this day.
From Saint Andrew Daily Missal:
The word Epiphany means manifestation, and just as at Christmas, it is the mystery of God appearing in visible form; only no longer does He show Himself to the Jews alone but “on this day” it is to the Gentiles that God reveals His Son (Collect). In a magnificent vision, Isaias beheld the Church as typified by Jerusalem, whither should flock kings and nations, “the multitude of the sea” and the “strength of the Gentiles”, coming from afar with countless caravans, singing the Lord’s praises and bringing Him frankincense and gold (Epistle). “The kings of the earth shall adore Him, all nations shall serve Him” (Offertory). In today’s Gospel we see this prophecy fulfilled.
While at Christmas we extolled the union of Our Lord’s divinity with His humanity, at the Epiphany we honour the mystic union of souls with Christ. “This day a star led the Wise Men to the manger; this day water was turned into wine at the marriage feast; this day Christ chose to be baptised by John in the Jordan for our salvation, alleluia.”* So we read in today’s liturgy which thus connects this feast with that of the Octave Day and of the Second Sunday after the Epiphany.
At St. Peter’s where are the relics of the Church’s first visible head, the liturgical celebration of the entry of the Gentiles into the Church takes place. “In the adoring Magi”, says St. Leo, “let us acknowledge the first-fruits of our own calling and faith; and let us commemorate with hearts full of joy the foundations of this our blessed hope. For from this moment we have begun to enter our heavenly patrimony.”
* Ant. for second Vespers