The kA rating is the surge current the breaker can withstand in kilo-amps. A normal breaker will see several thousand amps in a short condition. The breaker must be able to withstand and break that current safely.
This is correct. Look at your 15A, 20A, 30A breaker, and on the OFF side you'll probably see etched in there "10kA" or some such. The breaker will take 10,000A of power, guaranteed. It might take 12,000 or 15,000, but it will definitely
take 10,000. Anything above its throw value it will throw and cut off the current flow--to protect from fire, not to prevent damage to appliances or injury or death. GFCI is for fast-throw (because neutral/hot are passing current 20mA or so out of sync, so the current is going somewhere it shouldn't be). Panel surge suppressors direct excessive surge (40,000A or so) directly away from the panel and to ground.
the 10kA value basically says that anything above those 10,000A they're not guaranteeing is going to work out for you. The breaker might throw and the current arcs across the poles anyway. Maybe it doesn't even throw, it just welds in place. Or maybe it throws, and cuts current, and then you replace the breaker because it doesn't work anymore.
Panel probably got hit by lightning. I can't comment on how much power flowed through--about 12 breakers blew out, but they're all in parallel. Extremely high voltage found 16 paths to ground, and sent more through things that would fail faster (easier to arc, so lower resistance), and then ran out of juice. The more paths to ground, the faster current flows and the faster the surge is over. So at some point, that panel may have passed 120,000 amps; I doubt it. Maybe the first few breakers blew, arced, then became high resistance. Around 30,000 amps passing, mainly going to 2 breakers, blows them out and cascades to the next 2, while the rest bleed 9000 amps all together. Boom boom boom, and there goes your electric panel.
The worst failure mode is when the spark jumps the gap and you get 10kA flowing through a fused breaker into your appliances and your house catches fire everywhere because the wires melt and ignite the frame. Rare. Very rare. The surge should be over too fast to create fires, not fast enough to save your appliances.
That's what the whole house surge protector is for: under high current conditions, it provides a clear path directly to your grounding rod. Most of that current flows straight out of your panel; the rest should throw breakers. If the surge is high enough voltage to actually increase current flow--even without throwing a breaker--it means you're burning stuff out. Think your 110V wall socket becomes 220V and you plug your TV in? That's what happens, and your TV draws 1/2 amp and the breaker will throw at 15 amp and so now you have 1 amp and the breaker ... does not care, happily lets your TV fry. So, $2000 refrigerator? Water heater? Sump pump? You add a surge suppressor at the socket as well to feed back to ground.
Stay the hell away from electricity.