what is a stair nose

Just in case you are wondering, here' s a couple of pictures of a "stair nose" (stairnose?)

One is a view looking from the family room into the kitchen. The pantry is on the left. The strip of wood on the edge of the tile is the 'stair nose'. In the old kitchen, it was a piece of grooved metal, with screws holding it in place. Pretty ugly, and impossible to clean. The wood will be stained to co-ordinate with the new cabinets.

The other picture is a close up, showing how the wood wraps around the edge of the step to the kitchen.

The reason the wood does not extend to the wall on the right is because a low cabinet will be installed there. I do not know why the trim was not placed all the way over so the surface was level for the cabinet to sit on. Another question for the contractor.