Most of the Aeneid is recounted by an omniscient narrator, who, with the help of the Muses, is able to recount events in the distant past involving both gods and mortals. He is also able to look into the hearts and minds of his characters – both mortal and immortal – and tell us what lies there. (The narrator does speak in the first person sometimes – as in the opening line, "Arms and the man I sing" – but since he is in no way a participant in the events he describes, it still makes sense to call this a third person narration.)
Things get switched up a bit in Books 2 and 3, where the narrator is Aeneas, who recounts his own experiences and adventures, beginning with the fall of Troy. Even though Aeneas isn't the most introspective guy, he does give us glimpses of his emotional reactions to things – and even takes us inside his dreams, as when he tells us how the ghost of Hector appeared to him on the night of Troy's destruction.