It's hard to even describe what The OA is about without being extraordinarily vague, giving away a spoiler, or just confusing yourself. However, theories about Homer on The OA could potentially unlock the series. Emory Cohen's character is one of the more mysterious figures.
Prairie and Homer meet as captives in Hap's laboratory. He followed Hap and agreed to participate in his study in order to raise funds for his then unborn child — one of the more believable reasons a character has to be accidentally kidnapped on the series. While he left evidence of his outside life in Hap's house, that evidence (a class ring) conveniently disappeared. His NDEs are the most similar to Prairie's, he also left the house during his captivity, and according to her story he received the second movement. He and Prairie are wildly different people with different upbringings, but their belief bonds them together.
He's not the only character on the show who raises questions about the mythology. There are also a lot of clues surrounding Rachel, Prairie's alleged fellow captive — and Riz Ahmed's character, Elias, the potentially suspicious FBI agent. However, since Homer and Prairie's relationship feels so important to the series, and "Homer" is the last spoken word in the finale, let's focus on him.
He And French Are The Same Person
What was that weird mirror scene?! Is French/Alphonso an alternate dimension version of Homer? That's a lot of names for one character. Theories about Prairie being in purgatory or an alternate dimension, or about Prairie's team having been deliberately recruited based on their similarities to Hap's subjects hinge on the comparison between these two characters in particular.
He's The Shooter
This is my own personal theory. What if Homer conspired to kill Prairie so that she could return to the other dimension and find her father? Then, Season 2 would be still be about getting back to Homer. There has to be a reason the armed man was around, and that his face was never revealed. Then, that could explain why the movements stopped said school shooter — though, I suppose a true believer would just accept the power of the movements.
I would also not be surprised if Scott somehow escaped Hap and went to do his part to help Homer and Prairie reunite — even if that logically lead to him posing as a school shooter.
He's Not Real
This would mean that Prairie is making the whole thing up, as French is lead to believe. Though, if that is the case, the fact that the reveal is an Illiad reference doesn't make sense to me. It's not like Prairie invented a guy named Hector, or Achilles, or even Troy. Homer was a verbal storyteller. I get that Prairie is also a storyteller by this theory, but you don't really learn about Homer by reading his famous works. Also, why The Illiad and not The Odyssey? The latter is a story about trying to get home. The former is just a war epic. If the book is research, it is an odd choice of research. If the book was planted by Elias or someone else, it's a bad plant.
There is evidence to suggest that his name isn't Homer — his vision told him that much. Does that just mean that he has an angelic name like The OA, or is it evidence that Prairie made him up? Odd that Prairie would include incriminating evidence into her own story, but that is just one of the many mysteries surrounding this particular character. If the show returns for a Season 2, some of these theories could help explain what the show is actually all about.