While the celebration of Christmas remains fixed on December 25 in the Catholic Church, the complimentary feast of Epiphany can be moved by the local bishop.
In the Roman Rite of the Catholic Church, Epiphany is primarily focused on the visit of the "magi" or "three wise men" to Jesus after his birth.
Traditionally this was always fixed to January 6, a day in the Eastern Church where three separate "epiphanies" are celebrated. Also, in some Eastern churches January 6 is focused more on the birth of Jesus.
January 2 - January 8
The US Bishops explain on their website that Epiphany is a moveable feast in the United States:
The traditional date of Epiphany is January 6, but in the United States it is celebrated on the Sunday between January 2 and January 8.
In other places of the world, such as Italy and the Vatican, Epiphany is always celebrated on January 6.
This means that for many Catholics, Epiphany is on the same date in January every year, but for Catholics in the United States, it can be on different dates, but always on a Sunday.