Extending Blow is a trick that sends Link hurtling towards a map's origin at a speed proportional to the distance from that origin. It is triggered by performing a Final Blow on an enemy which the game considers to be dead.
The setup for an extending blow is generally quite precise. The idea is to have an enemy who is standing close to the edge of a void (or a ledge over sinksand or lava), then perform a spin attack or jumpslash to knock them down. If the enemy lands correctly on the very edge, the game will allow you to perform a Final Blow, but then also calculate that the enemy is over invalid territory and kill that enemy. The result is trying to perform a Final Blow on an enemy that no longer exists, and so the game default's Link's target for the Final Blow to the origin, (0,0,0).
As Link's speed during a Final Blow animation depends on how far away he is from his target, the further Link is from the origin, the faster and farther an Extending Blow will take him.
Currently there are three uses for an Extending Blow:
The first trick saves a fair amount of time. The second can be useful in some routes that perform the Eldin OoB route. The third saves 2 seconds at best.