The creature sitting on Harry's bed is small, has bulging green eyes and bat-like ears, and is wearing a tattered pillowcase for clothes. Harry, still shocked by its appearance, recognizes it as the thing that was staring at him from the bush earlier that afternoon. The creature stands and introduces himself as Dobby the house-elf, and Harry invites him to sit back down on the bed. Dobby bursts into noisy tears at being treated like an equal by a wizard, and this noise causes the dinner party voices downstairs to falter slightly. When Harry comments that Dobby must not know many nice wizards, the house-elf begins to bang his head on the window, explaining his behavior as a self-inflicted punishment for speaking disloyally of his masters, saying that he was bound to serve them until he died.
Dobby praises Harry for being famous, polite, good-hearted, and modest. Harry denies the praise until Dobby makes reference to Voldemort (calling him "He- Who-Must-Not-Be-Named"). We learn that Dobby wants to prevent Harry from returning to Hogwarts, as danger awaits him there. Harry protests, but Dobby will only respond by nodding or shaking his head. Their dialogue is interrupted by Dobby stopping to bang his head once more. This time, his yelps of pain are heard downstairs. Vernon Dursley reprimands Harry, and Harry quickly hides Dobby in the closet. Vernon leaves, and the conversation continues. Harry is furious to find that Dobby has been collecting all of his mail from Ron and Hermione. Dobby explains his actions as an effort to deter Harry from returning to school. Harry replies that he must return to Hogwarts, and Dobby leaps off the bed and enchants a violet pudding, causing the dessert for the dinner party to levitate. Dobby then causes it to crash to the ground in a failed attempt to persuade Harry to stay put.
The Dursleys are livid. They become angrier when a letter is delivered by owl and dropped on to the head of one of the guests. The guests leave, and the party is ruined. The drill deal is off. Harry fears for his life, especially when Vernon reads the letter aloud, which warns Harry that it is against wizarding rules for him to use magic outside of school. The Dursleys no longer fear that Harry will use magic on them, and Harry is locked in his room with the window barred, and he is fed through a flap in the door. His life has now reached an all-time low, and even in his dreams he is plagued by thoughts of being caged and taunted. He dreams that the bars of his cage are being rattled, and he wakes to see Ron Weasley, his best friend from Hogwarts, right outside his window.
The appearance of Dobby demonstrates Harry's great fame and shows how Harry deals with his renown gracefully. Everywhere Harry goes, wizards recognize him and know his history. Books have been written about him, theories concocted. We see this in action for the first time here, when Dobby weeps at meeting Harry and finding him to be tolerably polite. On the other hand, we see how thoroughly and genuinely embarrassed Harry is by this sort of attention. He does not ask to be known, to be a figure and an exception; more often than not, it causes him annoyance and suffering. But this is a part of him, like his scar or his glasses, and he must expect it and make with it what he can.
Rowling allows us to learn the novelty and nuances of the magical world while Harry himself learns them. Harry is eleven when he first discovers that the world of magic exists and almost instantly he was steeped into its lifestyle; we as mere observing "Muggles" cannot know any more than Harry does as he enters this strange alternate reality, and by making Harry somewhat of a beginner in that reality, the author allows us to come to understand it gradually. Harry, before this moment, has never seen or heard of a house-elf. But he learns through interacting with Dobby, and we learn through watching him. This pattern repeats itself throughout the story.
When Dobby drops the dessert and leaves Harry to be framed for it, we see the depths of injustice that are possible within the Dursley household. Harry began the day feeling rather low and he ends it infinitely lower, and we see that outside the relative safety of the wizard world, Harry is quite impotent. He is ignored, abused, belittled; he cannot escape his aunt, he cannot free himself or his owl, he cannot control what is happening to him, and his lack of control makes the need for an escape to magic all the more pressing.