For me, the thing which strikes me the most is the way Duchamp has captured the movement of the human form. By including a nude figure the viewer can focuses more on the actual human itself, rather than unnecessary details.

The brown tones in the background of the picture combines with the nude aspect of the painting nicely to add to the natural feel of the painting.
But why the staircase? Maybe to create a contrast between simple man made objects and the natural feel that is created elsewhere. The cubism in this piece also delivers an unnatural feel.
Or maybe he just saw his wife in the nip and thought it'd make a good painting.
Make up your own mind on it anyway.