Christmas was an ancient Earth religious holiday in the Christian faith that celebrated the birth of Christ, the portended son of God. It also had roots in ancient pagan Earth religions as a celebration of the winter solstice. It was celebrated on December 25. Related celebrations often occurred on the day before (Christmas Eve) and the day after (known as "Boxing Day" or "Saint Stephen's Day").
Traditional Christmas celebrations often included singing "Christmas carols," decorating Christmas trees, drinking egg nog, and giving gifts. Though by the 23rd century humanity had mostly "moved beyond archaic religions", many humans still celebrated Christmas, with varying degrees of secularism.
Starfleet crews often had shipboard Christmas parties. In 2266, one such Christmas party was held for personnel in the science labs of the Federation starship Enterprise. James T. Kirk made an appearance, and ended up spending a romantic evening with Helen Noel after they met, danced and he talked about the stars. (TOS: "Dagger of the Mind")
Christmas was a big affair on Titan, and the celebration there usually included a spectacular fireworks display, increasing in intensity over the traditional "twelve days of Christmas". In 2348, the fireworks were so loud on Christmas Eve that young Timothy Sinclair could hear them detonating above Enclave J-12 from his underground living area. Fearing an attack, he hid in the enclave's access tunnels where he was found by Dr. Robert Blaisdell. Blaisdell explained the fireworks, and read "the Christmas story" from the Bible to Sinclair, telling him "It's the reason for tomorrow." Blaisdell gave the boy the Bible he read from, which Sinclair treasured all his life as his first Christmas gift. (Star Trek: Pendragon: "Midnight Clear", "Father to the Man")
After his departure from the enclave, Christmas became a very important holiday to Sinclair, though it was several years until he experienced a traditional Christmas with Ben Bartholomew and his family, while attending Starfleet Academy in 2358. Sinclair often spent the holidays with the Bartholomews. After his marriage to Jean Brennan, the Bartholomews usually joined the Sinclairs at their ranch in Colorado. Eventually Christmas at the ranch became a grand affair involving many of the Sinclairs' friends and adopted family. (Star Trek: Pendragon: "Midnight Clear")
Aboard the USS Scandalon in 2364, Captain Steve Tecklenberg held a Western-themed "Christmas round-up" on the holodeck for his crew. It became an annual tradition. Captain Sinclair later continued the practice aboard the USS Pendragon in the 2380s. (Star Trek: Pendragon)
In 2367, the Sinclairs spent Christmas in Ireland with Fionnula O'Brien (Jean's foster mother) and her family. It was the elderly O'Brien's last Christmas before her death. (Star Trek: Pendragon: "Midnight Clear")
In an alternate universe in 2370, the Cardassian helmsman of the Enterprise-D, Hirhul Mendral, attended an December Advent service in the weeks leading up to Christmas with his friend Sam Lavelle. This service was rather sparsely attended by crew members given the religion's fall from popularity in the post-World War III era, but there were still enough believers who celebrated in the religious sense to justify the presence of a Christian chaplain, Sandik, to reside full-time on the ship and lead worship. Mendral found himself moved to tears by the hymn "O Come, O Come, Emmanuel," which to him was deeply reminiscent of the situation faced by the Bajoran-occupied worlds of Cardassia, which he had fled when he was young. (Sigils and Unions: Catacombs of Oralius--"Captives' Ransom")
While trapped in the Nexus in 2371, Captain Jean-Luc Picard experienced a Christmas, complete with a Christmas tree, presents and dinner, with his illusory children and wife, before being shaken from his reverie and resuming his mission to stop Tolian Soran from destroying the Veridian system. (Star Trek Generations)
Romulans regarded gagh as "special occasion" food. During Christmas, Romulans used a birch as a Christmas tree, had all kinds of food from various worlds made, and ate so much gagh that they have eaten through a three-month supply for five people. (RIS Bouteina: "Merry Christmas")
During a stay at a Lyran starbase, the crew of the RIS Bouteina was challenged to a hockey game being played on Christmas. To this end, they formed the Praetorians to play against the Lyrans' Wildcats. The Praetorians won the game 9-8, with a Kzinti bank as their Christmas gift. (RIS Bouteina: "A Hockey Game Broke Out")