A Christmas present was a gift given on Christmas.
The Eighth Doctor gave Susan Campbell a Christmas present: the Aztec bracelet which Cameca had previously given to him as an engagement present in Mexico in the 15th century. (AUDIO: Relative Dimensions, TV: The Aztecs)
The Eleventh Doctor hid a time window inside a box. He gave it as a Christmas present for Madge Arwell and her children, Lily and Cyril, so they could visit one of the most peaceful planets he knew. (TV: The Doctor, the Widow and the Wardrobe)
Bill Potts gave the Twelfth Doctor a rug as a Christmas present. (TV: The Pilot) Though he later claimed to have hated the gift, (TV: Twice Upon a Time) the Doctor kept it in his office, and parked his TARDIS on top of it. In return, the Doctor got Bill photographs of her late mother, as she had none. (TV: The Pilot)