This, combined with the fact that there's two Elis at the end of the trailer and the fact that Skull Face seems to be a strange apparation in some scenes, leads me to believe that:
Dealing with aspects of yourself that you hate will be a major theme in TPP. The whole "evil persona" was introduced with Liquid as Solid's foil in MGS1, which will again be given greater focus here, with Eli growing to hate David for taking everything from him. Big Boss himself will struggle with his Vader-esque Big Boss persona we know from the later games in the timeline. Given the psychological horror/mindwarping we've seen since TPP reveal trailer, the concept of dealing with the undesirable aspects of one's self will be visibly represented by doppelgangers. Skull Face likely represents the evil side of Big Boss, sharing similar ideology and line-crossing behavior, and Big Boss realizes how similar he is becoming to him and begins to converse with him in his mind as he begins to accept that they are the same. I particularly like the theory that Skull Face is real, and killed by BB early on in the game, but continues to haunt him due to his actions and - this is a big one - his words towards Snake. He probably gives a speech that resonates with BB, and BB doesn't like the fact that he agrees with him or sees his point one bit.
The two Elis at the end were likely symbolic. There's "another Eli" out there similar to how Skull Face will be "another Big Boss". The struggle isn't exactly the same between characters, but it is similar.
That's my half baked theory.