It is often used for school projects because of its flexibility. Another place it is used is in the shopfitting industry. Flexible MDF is usually used for indoor applications because of its poor moisture resistance.
MDF is generally cheaper than plywood and the surface of the MDF is much smoother, so it's easier to paint plus you won’t get any splinters.
The difference between long and cross-grain is the direction that the board bends. long-grain is vertical and cross-grain is horizontal.