The notion of progressive collapse is important for loadbearing structures. It means that when one element collapses, it triggers the collapse of a next element, and so on to bring down larger parts of the building or even a complete building.
Progressive collapse can occur because if one element is weakened by the fire and fails, the loads (mainly the weight of the building and its contents) are redistributed to surrounding elements. It means that those surrounding elements undergo an increased load, which could in turn cause them to fail. Since the remaining elements decrease in number, the loads on those continue to increase. This process will often repeat itself, causing collapse potentially also beyond the part of the building affected by the fire.