This is the best explanation we were given:
INMAN: Electromagnetism, geologically unique. The incident -- there was a leak. So now the charge builds up and every time we push the button it discharges it before it gets too big.
DESMOND: Why makes us do it -- push the button? If we, if we can just...
INMAN [laughing and closing the lid]: Here's the real question, Desmundo -- do you have the courage to take your finger out of the dam and blow the whole thing up, instead?
So, it appears the INCIDENT caused a leak in the electromagnetic "rock" (or whatever it is behind the wall) that - for some reason - causes a magnetic charge to build up (all the sudden getting really strong at 108 minutes) and that energy is discharged by pressing the button every 104-108 minutes. The count down timer resets when the buttons is pressed, and shows red and black egyptian hieroglyphics - for whatever reason - when the timer has expired which translates to caus. DIE. The FAIL SAFE is a SYSTEM TERMINATION system, that apparently, terminates the electromagnetic build up for good by blowing the whole thing up. Apparently, there is some risk in doing this - but what that risk is, is unknown.
