A repost of an /r/teslore comment of mine that's entirely applicable here:
A bit of explication, as I know this isn't a lore forum, yet understanding Talos involves heavy stuff.
Dragonborns are semi-divine. Hjalti Early-Beard (the mortal alternately known as Tiber Septim and Talos Stormcrown) was Dragonborn. That's a good foundation.
Shezzarines, the mortal reincarnations of Lorkhan, are also semi-divine. Halti and both his Underkings, Ysmir Wulfharth and Zurin Arctus, were all Shezzarines.
Enantiomorphic trios (most prominently known for Aka/Lorkhan/Magnus) are divine and mythically powerful events. The Rebel, who is invariably the victor, always becomes a Ruling King of the World. An Enantiomorph played out when Hjalti the Rebel usurped Wulfharth the King, who up to that point had been his real ace-in-the-hole power-behind-the-throne, in the process accidentally maiming Zurin, the Observer who witnessed the event.
Talos had access to and full control over the Numidium. Anyone who's studied Mannimarco, the King of Worms, knows that ambitious mortals can steal godhood with the power of Numidium-activated Dragon Breaks. It's not even necessary that Talos did this; the point is that he had it available to him, and it alone is fully capable apotheosis machine.
Talos had CHIM, which Heimskr and Mankar Camoran can both tell you. This alone entitles one to godhood and a sort of shackled omnipotence.
Talos's divinity ent just some Imperial propaganda. He has so much divine power that the Thalmor can't set about their Mundus-uncoiling scheme while he still exists; thus, they lie about him, and try to weaken the mythopoeic influence of Convention 2.0, the Enantiomorph of Talos, through stamping out mortal worship of him.
When your minds get done exploding, I'll answer all your questions. Note that not a single thing I referenced originated in an out-of-game text, so leave your canon bickering at the door. It's all true.