MDF stands for medium density fiberboard. It's a manufactured wood product that has superior properties than plywood for most reprap projects. It's fairly strong, will not split among any wood grain, and has a less of a tendency to warp.
Quite a few RepStraps use MDF as a Thick Sheet or frame material or both. For example the Wedgewood, the Mendel90, some versions of the Prusa i3, some versions of the Rroofl, the Duct Tape RepStrap, the RepOlaRap, the SGBot, the BasicMendel, the Y Bed Simplified, the Huxley Seedling, the MegaMendel, the ORE-Bot, the RedBot, the WhiteAnt, the A5 Powder bed printer, the Sumpod 3D, the Repemaker, the Farynozzle2.0, etc.
Most of the so-called PlywoodRepRaps are actually made out of MDF rather than plywood.
MDF is one of DarwinsSuccessfulElementsWorldwide.
One FutureToolIdeas with a lot of potential is a Milling and Drilling Head able to cut MDF parts. Several researchers are designing CNC Mills mostly built of CNC milled MDF, that are cable of cutting most of the parts for the next-generation CNC mill -- this is a different kind of RepRap, not merely a RepStrap.
The PrintItStickItCutit technique is a popular way to cut parts out of MDF using an ordinary paper printer and hand tools.
Some researchers prefer the kind of MDF that comes with a melamine coating on both sides. (Is the "veneered white MDF" mentioned at Y Bed Simplified actually a melamine coating ?)
More info on Wikipedia: medium-density fibreboard.