A casemod is where you modify a computer case so it's wild, wacky, and unexpectedly unlike how it was manufactured.
It's geek hotrodding.
Extreme casemodding means you start with a stock running computer... and you end with that computer in a modded case... and you have continuous uptime. No power outage. No resets. etc.
When you can get a ATX powersupply with a 30second UPS builtin, this will be alot easier I imagine...