Although it is not stated, the veil is a gateway to the "Afterlife". Both Harry and Luna can hear voices from the veil, but others can't. Perhaps they are hearing loved ones? Also Dumbledore refers to the room with the veil in as the "Death Room". Finally Luna also says something along the lines of "It's not like you'll never see your godfather again, remember those voices from the veil?" (I can't remember the exact quote, and I CBA to get the book).
When I first read the book I though Sirius had been hit with Avada Kedavra because it does not say what colour the spell was I assumed it was green (it just says "another flash of light"). But apparently it was a stunning spell.
I can only assume that when Sirius fell through he passed into the afterlife, thus he died.
This is only speculation of course, after all, it is the Department of Mysteries!