The dust is sharp and cuts into the shells of exoskeletons allowing the moisture to come out.
If you hit one with a pinch of powder, it's done.

Boric acid is another roach killer.
Not real toxic, they use it in eye surgury.
It is the primary ingredient of roachpruf.

I've dusted houses with roachpruf that had trails running across the walls, it took a month, but they were gone for 2 years after that.
Both are very effective for most household pests.
Neither is a danger to you or the pets at household exposure levels.
Just sweep the powder into the corners and under the cabinet drawers.