Who is Percy talking to in his dream in The Lightning Thief ?

Given that Percy is a demigod, his dreams give him the chance see into the lives and challenges of the immortals. Many of his dreams act as a pathway into him realizing who he truly is: a demigod (or half-blood). His mother is Sally Jackson (a mortal), and his father is Poseidon (the Greek god of the sea).
Percy's dreams are representative of "gifts" from the gods giving him much-needed information about both who he is and the lives of his immortal relatives. In one dream, Percy sees a "girl with curly blonde hair" hovering over him. She is feeding him pudding (which makes no sense to Percy). She asks him about the summer solstice. In the same dream, a "husky blonde dude" is there, covered with eyes. While Percy has no clue what his dreams mean, or who the people are, the gods are using his dreams to communicate with him.
Percy has many dreams before he finds out about his mythical origin. Most, if not all, of his dreams are meant to offer him hints into his origin and his task in saving those around him, if not the world.
At one point, Percy does identify as Hades as a person from his dream. He finally realizes that his dreams have played an important role in him finding out who he really is, who is after him, and what is at stake.
Essentially, Percy's dreams allow him to communicate with the gods or witness the battles between the gods.