The plan of the main keep is in the form of a cross with the staircase at its center.
The picture includes our recent visitors, Harriett and Tom, and Ken standing in front of the stair. They were admiring the second floor's coffered ceiling, I think. You can see two balustrades in this portion of the staircase. The section closest to floor level (where you see the people descending) is one stair, and the balustrade directly above that is along the second stair. Both stairs wind around a central light well above which is the windowed lantern in the top center of the castle.
They say that the stair was inspired, if not designed, by Leonardo da Vinci. I'm not sure anyone knows for sure.