Why would water facilitate the passage of kidney stones?

Because water will flush the stone to the urinary tract.

Water can push the stone and lubricate the way, make the passage easier. The water can also dissolve some stone, make it smaller. Stone is made because the water content is too low and make the concentration of solute become higher, make it easier to precipitate. An acid/base pH water would dissolve the stone easier, depends on the stone composition.