When I first saw this photo, my reaction was that a designer or architect was being unnecessary clever. But after studying it, I realized it is an eminently practical solution to a problem.
The problem being an extremely steep rise/run ratio for the location of the stairs. The distance from the front step to the hallway behind is short, the vertical distance to be traversed high. The choices would be extremely tall steps, extremely narrow steps, or perhaps a ladder/spiral staircase/other design.
I found more information at Fine Homebuilding, which discusses the practical aspects of stairway dimensions and also includes this interesting one:
Related: newel post.
Addendum: An interesting and authoritative comment from reader Lars -
"I built one of these as the replacement staircase to my basement. my 1829 house was moved to a new foundation in 1915. the basement stair location under the main level staircase approaches the foundation wall. the previous case used a landing and a 90 deg turn. this could only be negotiated without ducking ones head if you were under 5 foot tall. the alt tread case with comfortable wide treads uses half the normal needed run. this allows me to walk upright for the entire flight and get feet on basement floor with a 3+ foot distance from the foundation wall.
3 caveats. one must be able to lead with both feet. NEVER attempt to turn around mid flight. use of these stairs is much easier with handrails on both sides. I made mine as a utility purposed design with a center a center stringer that you must straddle. this rail has allowed me to move/slide large heavy objects up and down the staircase- both a refrigerator and a freezer - with use of a rope block & tackle. once you are familiar with the stair, it is actually easier to hand carry large boxes down that obstruct your vision. you never need to step past the tread you are standing on to get your other foot onto the next tread. leg motion is a straight drop. never stumble over the nosing."