Why didn't the breaker trip?

You might check to see if you have too much pluged into the cord, it may have overheated and started on fire. Those triple tap cords are not very heavy. The snap you heard may have just been the insulation on the cord finally bursting into flames and not have been a short at all

And as a forethought you have to remember that not all breakers react the same way. Some you cant get to trip even if they have a direct maintaned short while others will short just by looking at them wrong. Anytime you get a arc too neutral from a hot wire it should trip the brkr or blow the fuse because the arc itself will reach the trip level of most brkrs in micro seconds so I still think it is the coating on the wire bursting into flames that made the snap sound

Sometimes breakers are faulty... often, in fact. Also, they can trip and still look like they're "on" at the panel. (Of course, if other appliances/lights on the same circuit were getting power, you'd know the breaker didn't trip.

Another possibility is that just the burnt cord heated up. If the house wiring didn't overheat, the breaker isn't going to trip.

The materials burning at the hot junction (fire)

Just happened to burn at a rate less than 20 amperes. If the burn off of the small wires did not short constantly to ground and burned and consumed only say 19 amps or less then the breaker only recognized a load draw of more than 20 amperes and didnt trip.

Simple you had something catch fire at less than 20amp.

fire doesn't constitute a short circuit..