Storage is a glitch that affects the next event that occurs. You can enter the "normal" event state while still having a cutscene playing in a variety of ways. If the cutscene ends while in the "normal" state, you keep the property that would normally send you back to the "normal" state after any event. The next event that you activate will put you into the "normal" state instead of the state of being in an event, causing the event to be either "stored" or deleted, depending on the event. When activating another event, typically pulling out the Wind Waker or talking to another person, it will play the stored event instead. Some of these events will give you storage back when they finish playing, some will not.
In both the Helmaroc and Molgera boss battles, the camera pans to show the boss's death animation once it is killed. However, if Link dies right before this happens and doesn't game over by zombie hovering, the animations will play, but the cutscenes will not start, as Link is dead. Once the animation of the boss's death finishes, the camera will appear to snap away and back to Link very quickly, as the game has attempted to cancel a cutscene while there was no cutscene being played. This means that Link now has storage.
In the Ganondorf Boss Battle, Princess Zelda has a textbox that can be activated at the same time Link is able to pull out the Wind Waker. After this happens, cancel the Wind Waker and do a backflip immediately, then pull out the leaf to cancel the text while in the air. The text will now be stored and you can reactivate it by pulling out the Wind Waker. Canceling it after reactivating it with the Wind Waker will result in storage.