At the same time, Christmas will be written and printed a billion times as what some people call an eye-sore of an abbreviation: Xmas. This neologism was first recorded in 155. But, then, the X in Xmas is a very old abbreviation for Christ. An X-like character in the Greek alphabet is called chi (pronounced kee). Theologians have used chi as an abbreviation for Christ (Khristos in Greek). Christianity was recorded written as "Xianity" as early as 1100.
The other explanation is that in the Middle Ages few could read or write, and some of these people would make "their mark" (thence the origin of the phrase) making an elaborate mark or stylised scrawl as their signature. Those not able to do so simply drew a cross, the symbol of Christ, on the paper and then kissed it. Kissing the X represented an oath to fulfil obligations specified in the document, and the X and the kiss eventually became synonymous. This X symbol was known as the Christ-cross, which later turned to "crisscross" and X also found its way into Xmas. That is why Xs sometimes (esp. at the end of a letter) signify kisses.