We were taught in school that the 'X' here is being used to represent first letter of Χριστός, Christós, the Greek for Christ, and so Xmas is just short for Christmas. This explanation certainly seems to be true and until tonight I never gave much thought to how long the abbreviation has been in use or why it was adopted.
The OED gives a citation from 1551 using the form X'temmas (which makes it clear that we are dealing with an abbreviation). By 1660 we have Xtmasse and by 1721 the modern form Xmas had evolved.
But from the Etymonline website we can get a little further information. The Anglo-Saxon Chronicle of about 1100 uses the form Xres mæsse and apparently an in Old English an abbreviation for Christ was Xr, or interestingly Xp, which resembles the fist two letters Χρ of Χριστός. So if things had gone slightly differently we might have ended up with Xpmas and talked about ex-ar-mas cards.
What I haven't been able to find out so far is whether Xmas is peculiar to English or similar abbreviations are found in other languages.