What is the origin of "xox"?

There are a number of claims as to how X came to stand for "kiss"; if you're interested you can read more at:

• How Valentine's Day Works

  How about the "X" sign representing a kiss? This tradition started with the Medieval practice of allowing those who could not write to sign documents with an "X". This was done before witnesses, and the signer placed a kiss upon the "X" to show sincerity. This is how the kiss came to be synonymous with the letter "X", and how the "X" came to be commonly used at the end of letters as kiss symbols. (Some believed "X" was chosen as a variation on the cross symbol, while others believe it might have been a pledge in the name of Christ, since the "X"—or Chi symbol—is the twenty-second letter of the Greek alphabet and has been used in church history to represent Christ.)

• Why Does X Stand for a Kiss?

  However, the prosaic explanation of this romantic sign may be twofold. Originally it represented the formalized, stylized pictures of 2 mouths X touching each other--X. But then, a little more complicated, the kiss entered the cross by a chain of events and really owes everything to men's lack of education.

  Early illiterates signed documents with a cross. They did so for an obvious reason. A cross was so simple to draw, and yet, being also a sacred symbol, implied the promise of truth. But to solemnly confirm further the veracity of what had been endorsed thus, the writer kissed his 'signature,' as he was accustomed to do with the holy book. And that is how, finally, by its very association, the cross came to be identified with a kiss.

• Online Etymology Dictionary

  As a symbol of a kiss on a letter, etc., it is recorded from 1765.