In your high school Physics class you must have learned that objects expand when heated. If you ever major in Civil or Mechanical Engineering in college in your Junior year you will take a class called Strength of Materials. About two weeks into the course you will learn how columns fail under vertical load. I won't bother you with the formulas but essentially the longer the free length of the column - the less load the column will carry.
In the same Strength of Materials class you will learn that the yield point of Steel, the stress that the steel will permanently deform, depends on the temperature. The higher the temperature - the lower the yield point.
Unlike the traditional "square set" steel construction the World Trade Center used core and tube structural system. The concrete central core and perimeter steel columns carried all of the building's loads. This allowed for column free floor plans that offered maximum of flexibility in dividing up the space. This is why the WTC's windows were 4 feet wide, there were vertical columns between them.
To save the weight and cost instead of solid I beams the engineers used lightweight trusses to support the floor slabs, instead of solid I-beams traditionally used in high-rise construction. These trusses were rigidly bolted to the center core and to the perimeter columns. In addition to supporting the floor slabs these trusses also provided lateral bracing for the columns, keeping the columns' free length to a single floor. The floor trusses, however, are particularly susceptible to buckle in a large fire. Part of the building's structure was intentionally left exposed at the observation deck so that the visitors could see how the building was built.
When the planes hit, they immediately cut a number of perimeter columns, shifting the loads they carried onto the remaining columns. The fire that followed heated the floor trusses which expanded. As they were rigidly bolted at both ends they had no place to go but to buckle sideways. When they did, the bolts failed and the trusses pulled away from their attach points. When that happened, the free length of the columns suddenly doubled or even tripled.
The columns, which were already carrying more stress than they were designed for and were also heated by the fire started to buckle, shifting the loads they carried onto other columns increasing stress on them. When enough columns failed, the remaining columns could no longer carry the weight of the building above them and failed all at once.
As the part of the building above the fire came down on the undamaged floor, the columns supporting the floor failed sending it crashing down on the floor below, causing that floor to come down on the floor below that, and so on and so on.