what is the name of the mexican christmas tradition

The name of the Mexican Christmas tradition you're referring to is "La Posada." It is a reenactment of Mary and Joseph's search for a place to stay during their journey to Bethlehem for the birth of Jesus. Participants carry a statue of the Virgin Mary in a procession from house to house, symbolizing the couple's search for shelter. At each house, they are welcomed with a party, complete with music, food, and prayers. The tradition is a reminder of the importance of hospitality and inclusion during the holidays.