The double overhand stopper knot (also called the "Lapp knot" or "stopper knot" in climbing parlance) is the standard backup knot used after a figure-8 follow-through tie-in. Where a single overhand has one wrap, the double overhand has two wraps before the working end is threaded back through. The extra wrap makes the knot significantly more secure under cyclic loading.
This knot is taught alongside the figure-8 follow-through in every climbing belay course. The reason: a figure-8 follow-through alone is acceptable but can theoretically untie itself under cyclic stress (rare but possible). A double overhand stopper knot eliminates that risk. The knot sits against the figure-8 and tightens under any tension, locking the figure-8 in place permanently for the duration of the climb.
The double overhand is also the standard stopper at the ends of rappel ropes — preventing the rope from accidentally passing through a belay device on the way down. This is a basic safety practice that has saved many climbers from rappelling off the ends of their ropes.