The main reason is its uniform density. The second reason, is its price. You can find a 4' X 8' sheet around here for about $20
For more info read the MDF FAQ.
There's nothing wrong with using real wood or plywood. Its just the benefits and low cost of MDF usually make it a preferred choice.
MDF is dimensionally stable...meaning it won't expand or contract with humidity changes. Also it is dense which is good for dampening. MDF mills easily and is readily available. Those are the things that come to mind quickly anyway.
Solid wood is not the best thing to make enclosures out of because vibrations travel through it easier than through MDF, particle board, or plywood. It is not just a matter of price. Because these woods are not one solid piece with a grain running in one direction, vibrations are not transmited as easily through them.