They never really say. You just sorta...get the mask and that's about it. It's just like...a nod to Adult Link and giving you a super-awesome reward for getting all the other masks.
There's theories that maybe it's Link's Termina counterpart, but, theories are just that.
The Wiki entry of the Majora's Mask manga (totally non-canon) says...
Of course, the manga isn't canon, and sometimes strays far from the source material, and what was written about the Fierce Deity was probably done as nod to Link.
Also - where do you see the Gerudo symbol on him...?
I was mistaken. I saw the crescent moon on him, and remembered it as the Gerudo symbol. It's been years since I've played the game.
Since there was no Opposite Link in that world, and since there was no Opposite Ganon either, I just thought of Link being a Garudo when I was playing this. That, and I got the idea from "Hyrule: The Legend of Zelda" site. (HTLOZ -- a now defunct site)
I just thought this was Evil Link when I first played through the game. Then the site offered the theory that it could be a fusion of Link and Ganon, which fits the all-around disturbing theme running through Majora's Mask.
And I still say he was partial inspiration for Dante. (Blade + Alucard + Fierce Deity Link)
Off Topic:
Alucard even had an evil doppelganger (evil twin) so, I'm not letting that slip by either.
In DMC3, they added the demonic tower, lava pits, and train track over the lava pits from Shadowman. You could even say that they even added Shadowman's shirtless look, but that's debatable.
You don't see the lava, but it's there underneath the track...
The Tower
I'll even go as far as to day that they took the idea of Beowulf from the lumbering Trueform giants you had to fight in SM.
But wait, there's more!
Vergil, is actually suspiciously similar to another Vergil... who was also the inspiration for Cole MacGrath, incidentally...
http://en.wikipedia.org/wiki/Static_(DC_Comics)
I guess it's just a knee jerk reaction to seeing another character with spiky hair, a blue trench coat, and the same name... and then people saying that it's completely original...
Sorry about the off-topic, it's just that this has been on my mind for a while, and I was watching SM vids... w/e