When passive fire protection is discussed it is usually in the context of compartmentalization, and keeping one area safe from the smoke and flames in a different area. The reason this is so important has to do with the different stages of a fire, and how the fire would be able to spread during those stages.
When the fire is first staring out it might be smaller and burn at lower temperatures. This may seem safer, but those low temperature flames cause significant amounts of smoke and toxic gases to be released. Considering that 70% of all fire victims actually suffocate, this smoke can be more hazardous than the actual flames.
The passive fire protection is in place to keep this smoke from being able to escape the compartment on fire, keeping occupants safe while they escape.
After the fire has been burning for a while, the smoke gas contained in the room will cause everything in the room to heat up significantly, and if this gets hot enough it can cause a flashover. A flashover occurs when every combustible element is simultaneously heated to a point that causes spontaneous ignition. This point can turn a slowly smoldering flame into a roaring fire within seconds, engulfing everything in intense heat that can be around one thousand degrees Fahrenheit.
During the flashover the gases and combustibles igniting is essentially an explosion, which creates an intense burst of pressure. Passive fire protection in place helps contain this pressure, and prevents it from being able to spread into other areas. This pressure has been known to blow open a closed fire door or shatter windows, and if the fire dampers and firestop are not properly installed the ventilation and holes in the wall can act like a chimney, with the super-heated air forcing its way into other areas.