Beware of crappy music
What happened in the video is that a guy copied a hacked save file from SD card to the Wii. After loading the game, the exploit was triggered when Link talked to a NPC. The black screen with text on it is where the game was crashed and a custom program was loaded on the Wii.
Since the exploit was on a game, it's unlikely that it'll be patched by a Wii update.
Note that it doesn't work newer copies of the game so get a preowned one if you don't already own one.
More info: http://wiibrew.org/index.php?title=Twilight_Hack