Desktop X refers to a desktop environment that uses the X Window System, which is the primary windowing system used by most Linux distributions. When someone says Desktop X, he's usually referring to the major desktop environments in the Linux ecosystem such as Gnome, KDE, ect.
So for example, this forum is named Desktop X, which means that this forum is for discussing problems you may have with the desktop environment itself. Problems like that involve something like unmovable windows, usability problems, missing taskbars, ect.