MDF is an engineered product that is made up of wood fibres bound together with resin and wax. Because of this, it is denser than plywood and stronger than plywood. As it paints very well, MDF is most commonly used as a paint grade material.
In terms of staircases, MDF can only be used for stringers, treads and risers. If you plan on painting or carpeting your staircase, MDF is a comparably cheaper alternative to hardwood and other timber types.