To 'stabilise' it you test it under a much higher load than you're likely to use in high end gaming. That way, if its stable then, you know it'll survive no problems.
Unstable CPUs crash. Ppl tend to call this phenomenon ''The Blue Screen if Death'. If it happens too often, its possible damage can occur to the CPU via voltage spikes, and this will permanently destroy your chip.
By checking for stability under complete or near complete usage levels you are basically showing proof that your OC is reliable enough to use under any conditions you are likely to see during actual usage.