Lens stop-down button is used to check depth of field, to check the aperture operation, to lock the aperture down and remove the lens eg for manual macro tubes, and it also fires a stream of flash pulses to check flash light modelling (on Canons at least).
I used to use it a lot with film as that was pretty much all you had to go on for DoF, but with digital a) you've got an instant LCD image, and b) on crop cameras the viewfinder is so small and dark you can see FA anyway. It's much more useful for DoF checking on full frame as you can see a lot bit more.