This photo is from Wiki, so you can see what the modern (built in 1932) Bramante Staircase looks like. It's a double helix design, modeled after the original built in 1505. It's purpose is to move traffic in two directions without interruption.
The original was built to accommodate animals and people, and to connect the Belvedere Palace of Pope Innocent VIII to the outside. Built in a herringbone paving pattern with granite doric columns.