Kidney stones form when solutes in the urine precipitate out and crystalize, and although these most commonly form in the kidneys themselves, they can also form in the ureters, the bladder, or the urethra.
Though I have in my life experienced gout, bladder stones, a botched bone marrow biopsy and various other screamable insults, until recently, I had no idea what pain was.
The pain is caused by the dilation, stretching, and spasm caused by obstruction of the ureter, and is typically worse at the ureteropelvic junction and down the ureter, and subsides once the stone gets to the bladder.
They considered the stones " passed" if they were bumped up to the point at the bottom of the kidney model, where they would enter a tube that connects to the bladder.