Someone who does graphic design, page layout or artworking for a living. It comes from them using Quark Xpress a professional grade page layout programme. Whilst Quark does have other software, its name is so associated with the Xpress application that most people in the industry just call it Quark (and maybe put the version number of Xpress behind it like Quark 6 for Quark Xpress version 6). It also sounds better than InDesign (as in Adobe InDesign, the major competitor to Xpress).

Its similar to a Photoshop jockey - someone who uses Adobe PhotoShop image manipulation day-in, day-out for a living.