In abbreviations, it can represent "trans-" (e.g. XMIT for transmit, XFER for transfer), "cross-" (e.g. X-ing for crossing; XREF for cross-reference), "Christ" (e.g. Xmas for Christmas; Xian for Christian), the "Crys" in Crystal (XTAL), or various words starting with "ex" (e.g. XL for extra large; XOR for exclusive-or).
Xmas has been used for hundreds of years in religious writing, where the X represents a Greek chi, the first letter of Χριστος, "Christ." In this use it is parallel to other forms like Xtian, "Christian." But people unaware of the Greek origin of this X often mistakenly interpret Xmas as an informal shortening pronounced (ĕksPRIMARY_STRESSməs). Many therefore frown upon the term Xmas because it seems to them a commercial convenience that omits Christ from Christmas. "Xmas" is frowned upon in modern guides for writing styles. Style guides at the New York Times, The Times, The Guardian and the BBC all rule out its use, where possible.
Soources: YourDictionary / Wikipedia