A triple fault is an event on x86 series microprocessors, where a fault occurs when the CPU is attempting enter the fault handler for a fault occurring during the course of some other fault handler. The microcode on the x86 series machines responds by re-starting the CPU, since this should 'never happen'.
Triple faults were the solution to a problem with the Intel 80286, which was that once they were in protected mode, there was no way to return to real mode. Causing a triple fault turned out the be the answer. This issue was fixed in the successor Intel 80386.