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)