Christmas is a holiday celebrated in Gotham City on the 25th of December, with some celebration the day before on what is called Christmas Eve. Notably, the Arkham Origins incident took place on the night of Christmas Eve and the morning of Christmas itself, with the first meeting between The Joker and Batman taking place just after midnight.
Christmas seems to be a time of rest and festivities, as seen from Alfred Pennyworth's frequent requests for Batman to turn in for the night to have a filling "Christmas dinner" and a piece of radio chatter where a Gotham criminal laments that he should be at home relaxing rather than patrolling the streets of Gotham. Christmas may also have some ties to goodness and morality, as Deadshot's hostage will protest to having a gun put to his head by screaming "It's Christmas," a statement that makes little sense unless Christmas is somehow tied to good will or mercy.
Christmas also seems to have a specific aesthetic, as several cosmetic changes are made to the map of Gotham City that are not present during the Arkham City and Arkham Knight incidents. Some of these decorations include long strings of small lights, large pine tress like the ones located in Jezebel Center, and red hats of the kind worn by Ricky "Loose Lips" LeBlanc.