As soon as Harry, Ron, and Hermione land in Hogsmeade, a shrill scream pierces the air. Death Eaters spill out of the Three Broomsticks and try to summon the Cloak, but it doesn't move. The trio hides in an alley and the Death Eaters agree to release dementors to find Harry. Hermione tries to Disapparate, but they can't. They see dementors coming and Harry conjures his Patronus. A voice tells Harry to get inside the Hog's Head and go upstairs. Harry obeys and he listens to the man tell the Death Eaters that the Patronus was a goat, not a stag. After an argument, the Death Eaters leave. The barman comes upstairs. He has piercing blue eyes, and Harry realizes that this is Aberforth. He has the other enchanted mirror, and he sent Dobby.
While Aberforth resembles Dumbledore primarily in looks and especially with his eyes, realizing that this is Dumbledore's brother gives Harry another insight into how a person can continue to affect positive change after death. Just as Harry continues to fight Voldemort, just like his parents, Aberforth has been furthering Dumbledore's goals by helping out Harry. All of this helps to rob death of its fear and mystery, as this shows it is possible to live (at least in some way) after death.
Aberforth brings the trio food and tells them to get out of Hogsmeade. Harry says he needs to get into Hogwarts and has to do what Dumbledore asked him to do. Aberforth notes that Dumbledore's plans often caused people to get hurt and tells Harry to leave the country before he dies. Aberforth says the battle is already lost and tells Harry to let someone else do his job. He asks if Dumbledore was honest with Harry, but Harry can't answer. Aberforth says that Dumbledore learned to lie as a boy and he stares at a portrait of a girl over the mantel. Hermione recognizes her as Ariana. Harry says nothing. He thinks that he chose to believe in Dumbledore's mission and has no desire to doubt now.
At this critical moment, Harry finally understands that dealing with Dumbledore's legacy is indeed a matter of choosing to believe or not. He can choose to allow Aberforth to derail him and cast doubt on Dumbledore and what he tried to do, or he can choose to reaffirm his commitment to Dumbledore and what Dumbledore asked of Harry. Choosing to recommit to his mission shows that Harry now understands that the only way to honor Dumbledore's memory is by completing this task and passing on Dumbledore's wisdom.
Hermione says that Dumbledore cared about Harry, but Aberforth spits that lots of people Dumbledore "cared" about suffered. Aberforth angrily says that when Ariana was six, three Muggle boys assaulted her when they saw her doing magic. It made her mad; she couldn't control her magic and was sometimes dangerous. She loved Aberforth and would calm down for him. She accidentally killed Kendra when she was fourteen, and Dumbledore returned home to care for her. He began to neglect Ariana when Grindelwald arrived and, finally, Aberforth put his foot down and refused to let Dumbledore take Ariana around the world with him. He and Grindelwald began to duel, Dumbledore joined in to stop Grindelwald torturing Aberforth, and Ariana died in the confusion. Aberforth doesn't know who killed her.
Ariana's story begins to show Harry that, while magic may be what gives people like Voldemort and Grindelwald their power, magic also has the potential to destroy a vulnerable young person like Ariana—and destroy her whole family's life in the process. It's also telling that Ariana died at a time when Dumbledore was dedicating himself to intellectual pursuits with Grindelwald; this suggests that there are consequences to leaning too heavily in either direction, though it may be safer to rely on knowledge than magic.
Aberforth says that Grindelwald left and Dumbledore was then free of his burdens. Harry says that Dumbledore wasn't free: the potion Dumbledore drank in the cave on the night he died made Dumbledore re-live the duel and plead with someone to hurt him instead. Aberforth tells Harry that if Dumbledore loved him, he'd have told Harry to hide. Harry insists that he hasn't given up, he needs to think about the greater good, and he knows how to finish Voldemort. He asks for help getting into Hogwarts. Aberforth sighs and turns to the portrait of Ariana. She walks back through her portrait and returns a few minutes later. The portrait swings open to reveal Neville.
In this moment, Harry also recognizes how uncertainty and tragedy can hobble a person: just as Harry has been occasionally too caught up in stewing over Dumbledore to dedicate himself to his quest, Dumbledore, it seems, was never fully able to move on from Ariana's death and suffered his entire life because of what happened. This shows Harry the importance of learning how to move on, however a person chooses to do that.