I didn't understand what the reveal of Ougi's true nature meant. There were many words, but I only got the sense that she's a (apparition) manifestation of some part of Araragi which he rejected sometime early in the series. I understood that at the end Meme decided to "officially recognize" her existence, but that's not important here.
What exactly does Ougi represent?
Ougi is Araragi's youthful foolishness manifested as persistent self-doubt and lack of love for himself.
This idea is transient throughout the occurrences of Ougi. She initially spawned after the events of Shinobu Time. That's when Araragi registers the idea that he could criticise himself just like how the Darkness criticises the world as the "principles of the universe". After her creation, Ougi spars with Araragi, nudging out fears and doubts he has had about his decisions and actions. He wants to make himself feel guilty for the events of the series because he chose to save Kiss-shot, Senjou, etc. This was the main theme for the Sodachi arc, in which Ougi was actually right, that he knew the reason for Sodachi's suffering all along but hadn't acted. Of course, this isn't always the case. Why was this important in the entire series? Because Ougi had the ability to undo what she thought were the mistakes that Araragi had made, even when the mistakes were natural to make; Gaen's gang knew this. There are some plotholes though, but those will be up to your interpretation of the story.
Secondly, Ougi being his lack of love for himself an important developmental point in Owarimonogatari 2. In Bakemonogatari, his lack of love for himself allowed him to be so selfless in saving the 5 girls that it caught even Meme off-guard, which is a reason why Meme left, sensing that an abberation like Ougi might appear. Throught the series, Araragi gets beaten and cut up in many ways to save others. In Owari 2, Araragi also foreshadows his inability to love himself in Hitagi Rendezvous even when he was able to love Senjou.
His development was in the subsequent arc where he saved Ougi from the darkness. Choosing to sever his arm to save Ougi was the ultimate act of loving himself, to finally hurt for no one but himself. This was when Meme finally comes back, to signify that this huge Arc that started with Bakemono has come to an end.
Ougi also tries to sabotage the relationships between Araragi and the girls. I'm not sure whether this has been explained so I will only speculate that I feel this is because Ougi reflects Araragi's childish mantra that "friends decrease my power as a human". Another hint that Ougi is Araragi's childish foolishness.
Ougi Dark is really similar to Suruga Devil and Tsubasa Tiger. They are stories about growing up by recognizing a part of themselves. Araragi recognises that he is someone who can criticise himself and hate himself, Kanbaru sees the fears she has harboured reflected within Numachi and Hanekawa embraces her imperfections (jealousy in this arc). Accepting this as a natural part of growing up brought the stories to their conclusions.
Ougi is actually manifestation Araragi's self-doubt. She, or he, is one part of Araragi where she always tries to reveal hidden/missing parts of Araragi's history. In one episode she claims to punishing liars which is essentially Araragi.
Another proof I can gave is her own catchphrase which I love. "I don't know anything, Araragi-senpai. It's you who knows."
