The word 'dragonborn' first appeared in the commentaries on the PGE1, from
Redguard:
Make no mistake, Talos (now Tiber Septim in resplendant Cyrodilic) is still on the ascendant. I now believe the oracles have been badly misinterpreted - Septim may indeed be the Dragonborn as foretold. The Mer must unite at last or be consumed one by one.
In
Morrowind, Varieties of Faith says this about the god Talos (Lady N's quoting the wrong bit):
Tiber Septim (Talos, the Dragonborn): Heir to the Seat of Sundered Kings, Tiber Septim is the most important hero-god of Mankind. He conquered all of Tamriel and ushered in the Third Era (and the Third Empire). Also called Ysmir, 'Dragon of the North'.
As far as I am aware, "dragonborn" is used almost exclusively to refer to Tiber Septim and his descendants - in the one exception, the Nerevarine prophecies say that he will be "dragon-born," meaning born of the Imperial Province, as the player character is. What's important to take away from this is that while
Oblivion tried to tie this together with the covenant of Alessia in a really inelegant and poorly explained way, the word "dragonborn" has
always meant the Septims, and any different application is a new invention.
But that obviously leaves a large, unanswered question: what is it about Talos that made him "dragonborn." Ideally, this would have been expounded upon by
Oblivion, the game theoretically built around the rise and fall of the Septim dynasty, but because Bethesda was attempting to acquire a greater market share in 2006, what we are left with instead are a few scattered notes. Qawsed Asp quotes the most relevant.
The character Nu-Hatta is an important Moth Priest, which means he can read the Elder Scrolls. In the cited text, he briefly discusses the different gods who were alleged to have mortal origins. There's a pretty critical typo in The Imperial Library's version, so I'll requote it in this post:
"The Stormcrown mantled by way of the fourth: the steps of the dead. Mantling and incarnation are separate roads; do not mistake this. The latter is built from the cobbles of drawn-bone destiny. The former: walk like them until they must walk like you. This is the death children bring as the Sons of Hora."
This is extremely obscure and can be hard to understand, but the crucial line is towards the end, Tiber Septim became a god by "walk[ing] like them until they must walk like you." That is to say that his apotheosis was a sort of self-actualization, by his own willpower he
became a god. He did not acquire it through some ancient ritual by which a greater power gifted the godhood to him from on high, he stepped up and built it for himself. So he did not receive Akatosh's divine blood so much as he made his own blood as divine as Akatosh's. In a certain sense, this can be seen as the democratizing of divinity: in America, we are told that anyone can be president, in Tamriel, anyone can be a god.