No, this isn't the Zelda series back story, sorry. That story is far to long and convoluted. Further, though there is a chronological order to the Zelda games, no one has officially confirmed a timeline yet. The only thing we know about this game is it takes place “100 years after Ocarina of Time.”
With that out of the way, back the purpose of this section. This game was originally set as a Gamecube release title, due out in 04. However, because the Gamecube was on it's last legs anyway and Nintendo's new console (Wii) was coming very soon, they delayed and delayed till it was finally announced as a launch title for the Wii.
This caused a problem, however, as they couldn't leave Gamecube owners hanging. So, they released the original version of Twilight Princess on the Gamecube.
Since the Wii's version used the Wii Remote to control Link's sword, they determined that Link should hold his sword in his right hand to correspond to the majority of people playing. This caused a problem. It would be to time consuming to re-program the game to actually make Link left handed (yes, link is RIGHT HANDED in other Zelda titles), so instead they took the entire game coding, and mirrored it.
*THIS IS THE IMPORTANT PART*
So in the Wii version, left is right and right is left. Since this guide is written for the Wii version, if you are playing the Gamecube version every time I say “right” read it as “left” and vise-versa.
Other then this and the control scheme, the Gamecube and Wii versions are identical, though the Wii version does support 480p and Widescreen modes, while the Gamecube version does not.