The riser is the vertical surface of the stair. The tread on the other hand is the horizontal surface of the stair and the part of the stair you step on.
Nosing is the portion of the tread that overhangs the front of the riser. Often a stair builder will talk about the rise and run of the stair. The rise is the vertical dimension from tread to tread, while the run is the horizontal dimension from riser to riser (not including the nosing).