This technique allows you to pull out a deku stick away from a flame and still have it become lit. This effect can be carried anywhere Link can go with a normal deku stick. Flame Storage only appears to be storing the flame in your sword.
Here's how it works: One of the hitboxes for the sword becomes detached over the torch when using flame storage. Technically we don't "store" a flame at all, it just looks that way. When you draw a deku stick, it immediately checks to see if that stick is colliding with a flame graphic and if it is then the stick is told to burst into flames. Well... when you detatch the hitbox over there, then the game checks that location to see if there is a flame there.
What this means is that if you move far enough away to where the flame is no longer loaded, then the deku stick will not catch on fire when pulled out, but even if you go far enough to unload the flame, if you come close enough to load the flame again then it will still work. Swinging your sword, or leaving the area (by load), and quitting and reloading will all reset the hitboxes however, so flame storage will be cancelled under those circumstances. That said, there are 2 known methods to detach your sword's hitbox on a torch:
If it worked, you should be able to move away from the flame and the deku stick will still light when you pull it out again. Note that if you unload the area where the torch was before pulling the stick out it will not work until the flame is loaded again.