I first noticed this in the Journal under the heading Recusant's Sigil (obviously the x) but when I went back and battled Xemnas as Sora again, I was able to make out just what Xemnas was saying as the battle was preparing. "As your flesh bears the sigil, so your name shall be known as that of a Recusant." Is this touched on in other games that I haven't yet played (previously only owned 358/2 Days, Re:coded and 3D, but I just recently bought 1.5 Remix) or is it explained somewhere?
This term isn't mentioned directly, but the concept of it has been around in the series.
Recusant: "A person who refuses to submit to an authority or to comply with a regulation."
This can take on multiple meanings depending on how you look at it, and "submission" is a big keyword in all of this.
Xemnas marked all of the Organization XIII members with the Recusant's Sigil, a sign of the loss of their human selves (and probably their refusal to follow the orders of AtW since they all disobeyed his orders to stop the experiments). This sigil is represented by the letter "chi", which obviously relates to the X-blade. (There are likely deeper aspects we are supposed to take from "chi" but that's not what you are asking about)
Then there is the fact that Sora himself has not complied to Xehanort's plans since KH1.
Xehanort himself is something of a Recusant, having disobeyed the orders of his Master and shed his armor in the darkness, and went against the precepts that Keyblade wielders swear to follow (i.e. don't cause Keyblade Wars yada-yada)
(And although this is more like an analysis, Terra was recusant to both Eraqus and Xehanort, Eraqus to Xehanort, Ven to Xehanort & Vanitas, Riku to Xehanort/SoD, etc. and they all coincidentally have an "X" somewhere on them. The glossary notes that we've seen examples of the sigil and its meaning throughout the series, so it isn't a farfetched idea but nothing has been proven.)