Spoiler :
It's easy enough to deduce that it's a part of his spirit that he locked away inside Naruto.
If you look at the Third's example of the technique: The third locked the spirits in the death-god's stomach. The fourth did the same, but locked his spirit along with the foxs' inside Naruto instead.
He had to set the seal to release his own spirit when the fox had release eight tails for the simple fact that he probably can't stick around for long, and thus needed to conserve his time for the most drastic and last resort.
If you look at the Third's example of the technique: The third locked the spirits in the death-god's stomach. The fourth did the same, but locked his spirit along with the foxs' inside Naruto instead.
He had to set the seal to release his own spirit when the fox had release eight tails for the simple fact that he probably can't stick around for long, and thus needed to conserve his time for the most drastic and last resort.