Thermite, which is a mix of aluminium and steel, burns at a fierce heat. Give that the steel pre-existed in the building, and the planes supplied the aluminium and the ignition, you have the ingredients for a conflagration.
Fire needs oxygen, which would be drawn up the lift shafts by the hot air thus providing a chimney effect. This would be like blowing on a campfire to make it burn better.
All the ingredients for the disaster were thus assembled and we all saw what followed. However I do not give credence to the conspiracy theories regarding further explosives triggered at the base of the buildings.
The puff of white smoke seen at the base of one of the buildings could be explained by the fire blowing back down the lift shafts, which could be caused by an internal collapse, blocking these shafts and reversing the chimney effect.
There is a lot of facts and conjectures here
Giok