Mx. is a gender-neutral title used in the same way as gendered titles like “Miss” and “Mr.” Like the singular “they,” it’s used for people who identify as neither male nor female, or people who simply don’t want to be identified based on their gender.
It’s written like an abbreviation, but it doesn’t stand for any longer word; it’s just designed to look like other titles used before names, with the x used much like it is in statistics, to stand for an unspecified value (the person’s gender).