A Knox Box actually two things. When a builder builds a building, the build a hardened steel locker into the front of the building (set deep into the exterior wall) with a key-locked door. A master key to the building is placed inside and the box is locked.
The second piece is a Knox Box on the truck - it's a sturdy box bolted to the chassis with a radio activated (DTMF or digital burst code) to activate the lock. Inside this box is the key that opens all the boxes in the buildings that are keyed the same (or maybe a keyring with several keys).
When you get an automatic alarm in the middle of the night, instead of waiting on the keyholder or forcing entry, you call dispatch, the "pop" the box on the truck, you take out the master key that opens the box on the building, then use the master key to the building that's in the buildings box to get in and find the problem. Without this setup, either (A) the FD carries a thousand keys or (B) the building owner pays more for insurance, partly based on how long it takes a keyholder to get on scene (they figure either they pay for more fire damage due to delayed access or they pay for the damage the FD does forcing the door).
This setup allows the FD to carry only a few (or one) key (to the box) AND to maintain accountability for that key (shift captain can't take it home, chief (via dispatcher) knows who got it out last, and whe they put it back, etc. If the FD didn't maintain accountability for the key, they'd never put THEIR key in the building's box.