The
firestorm worked like this:
As a large number of incendiary bombs were dropped on the city center, a fairly sizable fire erupted. The Allies continued to feed the flames with bombs, soon getting several buildings burning. Eventually the flame reached a critical mass: The air convection caused by the source of heat, blowing hot air up into the atmosphere and sucking cool air in from beneath it, began to cause winds strong enough to suck debris into the fire -- and so the fire began to feed itself, and suck the air out of the buildings and even some underground areas of Dresden. There were people who died simply of suffocation because the fire took their oxygen away.
Once the firestorm became self-sustaining, the Allies could leave it knowing that it would feed itself -- it would do far more damage than a bomb (with two notable exceptions) ever could.