Harry is shocked, and stares at Mrs. Figg as she raves that Mundungus left to check on stolen cauldrons, leaving her, a Squib (a non-magical person born to magical parents) to protect Harry. She wonders what Dumbledore is going to say and tries to get Dudley to get up. Harry lifts Dudley and Mrs. Figg leads the way to the Dursleys'. Harry asks why Mrs. Figg never told him that she was a Squib. She points out that if the Dursleys knew Harry liked visiting her, they wouldn't have let him visit. Mrs. Figg worries about how to tell Dumbledore what happened and tries to impress upon Harry how important it is that he know immediately.
Learning that Mundungus was watching Harry and left confirms for Harry that the noise he heard was Apparation; now, he knows he's not hearing things or making things up. However, keep in mind that Harry had no idea that people were following him. This makes Harry feel even more like he's being left in the dark and not communicated with. This is also a surprise revelation about Mrs. Figg, whom Harry always disliked and never considered she could possibly know about the Wizarding world.
With a crack, Mundungus Fletcher Apparates in front of Harry and Mrs. Figg. He stinks of alcohol and tobacco and is aghast to learn what happened. Mrs. Figg hits him in the head with her shopping bag full of cat food and sends him to tell Dumbledore. As they reach the Dursleys' walk, Harry asks Mrs. Figg to confirm that Dumbledore is having people follow him. She does and then leaves him on the front porch. Harry rings the bell, Petunia opens the door, and Dudley promptly vomits. Petunia and Vernon help Dudley inside while Harry attempts to slip up the stairs unnoticed. When Vernon asks who hurt Dudley, however, he says "him" and points at Harry. Harry insists that he didn't do anything as an owl swoops through the kitchen window. Vernon angrily closes the window.
Given Harry and Dumbledore's previously close relationship, it's likely even more difficult for Harry to stomach that Dumbledore is ignoring him and having people secretly follow him than it'd be if anyone else did this. This speaks to the power and the strength of Harry's relationships with people other than the Dursleys. In light of their abuse, Harry has to turn elsewhere to get any sense of comfort, care, and guidance—especially given how unconcerned about Harry Vernon is here.
The letter is to Harry, expelling him from Hogwarts for performing the Patronus Charm. Harry decides he has to run away, since he'll never make it in the world without his wand and the Ministry will arrive soon to destroy it. As Harry tries to leave, he snaps at Vernon that he's expelled. Suddenly another owl hits the window and Harry takes its letter. It's from Mr. Weasley, telling Harry that Dumbledore is working on things and for Harry to stay at the Dursleys' house, not do magic, and not surrender his wand. Harry feels panicky but sits down and explains to Vernon who sent the owls.
Notice the difference in how Harry responds to news that Dumbledore and Mr. Weasley are looking out for him in comparison to how he speaks to Vernon. Again, this illustrates how neglected Harry is at the Dursleys' home, and how much Harry relies on and trusts the adults who care for him in the Wizarding world. This scene also shows Harry’s tendency to be impulsive and reckless, as he immediately considers throwing his life away and going on the run.
Dudley mumbles that Harry pointed his wand at him, things went dark, and then he started hearing things. He's unable to continue, except to say that he fell and felt cold and unhappy. Harry explains to Vernon that a dementor attacked Dudley, and Petunia adds that dementors protect Azkaban, the wizard prison. Both Harry and Vernon stare at her in shock, but Petunia saying this seems to convince Vernon that dementors are real. Another owl zooms through the window and Harry opens its letter, which tells Harry that his expulsion will be decided at a hearing in August.
The fact that Petunia knows what dementors are and what Azkaban is suggests that though she does what she can to pretend that the Wizarding world doesn't exist, she has a relationship to it that's much closer than Harry thought it was. This opens it up for Petunia to become more of an ally to Harry if she were to choose to become one, as she at least has some insight into how his world functions.
Harry tries to leave the kitchen, but Vernon insists that Harry explain what happened to Dudley. Harry patiently explains that dementors suck out people's souls, that you can't punch a dementor, and that he used the Patronus charm to get rid of them. A third owl, bearing a note from Sirius, flies in. The note says that Harry should stay put, which makes Harry extremely angry—he feels someone should praise him for fighting off two dementors by himself. Returning to his conversation with Vernon, Harry says he has no idea why the dementors were in the alley and he wonders out loud if they've joined Voldemort. Harry explains that Voldemort is back, and Petunia seems to comprehend the gravity of this. Harry is, for the first time, happy that she's his aunt.
Here, even though Petunia isn't kind to Harry and doesn't parent him effectively in any way, she's the only person who's able to make Harry feel heard. Harry's sense of relief at telling Petunia and having her believe him shows that it's cathartic to tell one's story—even if it's just the bare bones—and have someone else believe it. This suggests that being believed and being listened to is one of the most effective ways to heal and feel closer to others.
Vernon decides that with Voldemort back and dementors coming after Harry, Harry has to leave the house. Harry freezes; all his letters told him not to leave. As Vernon rages at Harry, another owl drops a red, smoking envelope—a Howler—in front of Petunia. It's addressed to her. After a moment, it bursts into flames, and a horrible voice says, "remember my last, Petunia." Petunia is silent and then says that Harry will stay. She briskly sends Harry to his room and refuses to answer Harry or Vernon's questions.
The Howler tells Harry and the reader that Petunia definitely has contact with someone in the Wizarding world—and that person has the power to dictate how and if she keeps Harry. Petunia keeps the sender of the Howler secret, though, attempting to maintain composure and a sense of power. Note also how little Vernon truly cares for his nephew—he’s willing to throw him out of the house and directly into danger.