MDF stands for Medium Density Fiberboard. It is a type of engineered panel used generally for wood working purposes.
It is created by breaking down real wood (hardwood and softwood) into little fibres. These wood fibres and then re-glued together under pressure to form broad flat boards. It is similar to particle board in this way, but with MDF, the fibres are so small that the final product is much more dense and has no air pockets like particleboard does.
The main uses of MDF in woodworking is its use as a substrate material. Because the glued fibres have no orientation, it does not expand and contract with humidity like natural wood. This stability makes it a wonderful product for the use as a veneer substrate. It also is produced with a very flat surface so there is no telegraphing of any undulations through a veneer.
Another advantage is that MDF is consistent and solid throughout its core. (Which makes it quite heavy by the way) This enables the product to be profiled by using a router for example. A sprayed on finish would need to be applied however for a final product. But this again is one of the benefits due to its perfectly flat sides.
One disadvantage of using MDF in the woodshop is due to the chemical composition however. It contains urea-formaldehyde which may cause eye and lung irritation when cutting and sanding, not to mention that it is listed as a possible carcinogen. Extra care must be taken for the respiratory system (i.e. a good filter mask) sop as not to breathe in the fine dust particles of cut MDF.
Also to note, if your shop is using a duct work system to collect dust from machines, the MDF dust will contaminate the entire collection of wood saw dust, so it would not be able to be used for other saw dust byproducts.
Specialty MDF products are also sold commercially such as a more fire resistant version , or a mold resistant version for high humidity areas, by changing the chemical makeup in the production process. These may have a different color associated with them other han the traditional light tan or gray.
Another specialty mdf product is the flexible mdf board that allows a wood worker to bend the board over of curved mold of some type. This is basically a regular board of mdf that has grooves or kerfs cut into one side leaving the other side wth its regular flat surface. (This image actually has a thin birch ply over on side of the mdf.)
It's advantages outweigh the hazards of working with this material however and it is a great addition to any woodworking lineup.