Harry returns to Hogwarts (in Dumbledore's Office, to be exact) via Portkey, while Dumbledore appraises Fudge with details of what happened in the Ministry.
Dumbledore arrives shortly, and Harry begins to suffer a HeroicBSOD. He ends up smashing some of Dumbledore's instruments and trying to escape through the locked door. He calms down when Dumbledore admits he's to blame for Sirius's death. Had he not explained crucial details to Harry earlier, Harry would have known that Voldemort would try to lure him into the Department of Mysteries.
Dumbledore first explains what we largely know: there is a connection between Harry and Voldemort's mind. Voldemort became aware that Harry could see into his mind on the night that Arthur Weasley was attacked. Dumbledore feared that Voldemort would try to use the connection in reverse. This was why he had been avoiding Harry and why he asked Snape to teach Harry Occlumency instead of doing it himself. Voldemort also conspired to use the connection to lure Harry into the Department of Mysteries.
Harry brings up another mystery: why Kreacher lied that Sirius had been kidnapped. Dumbledore explains that Kreacher had been serving more than one master. Fed up of being treated badly by his master, Kreacher was itching to escape. When Sirius told Kreacher to get "OUT!" in [[Recap/HarryPotterAndTheOrderOfThePhoenixC22StMungosHospital an earlier chapter]], Kreacher left the house to visit Sirius's relatives: Bellatrix and the Malfoys. As a house elf, he could never disobey a direct order from his master and could not leak information such as their headquarters. But he could tell them information that Sirius would not have realised was of any use: that Harry treated him like a father and was more willing to go to rescue him than anyone else. He then distracted Sirius when Harry was checking in the fire to see if Sirius was there.
Harry then turns on Snape. Dumbledore explains that when Harry cryptically told Snape that "He's got Padfoot!" in Umbridge's office, Snape did indeed understand what Harry had said and informed the Order.
Dumbledore now decides that the time is ripe for him to tell the whole truth as of why Voldemort tried to kill him. He begins by recapping the events of the previous books. He expresses regret that he never told Harry the uncomfortable truth and cared more about his peace of mind. It turns out that Voldemort tried to kill Harry because of a [[TheProphecy Prophecy]] made shortly before Harry was born. Though the prophecy record that Voldemort was trying to steal was smashed, Dumbledore can recall it clearly because he heard it being made, on the day that he interviewed Professor Trelawney for her job.
Trelawney's prophecy said the one with the power to defeat Voldemort would be a boy born at the end of July to parents who managed to defy Voldemort three times. It turns out that the criteria applied to two boys: Harry Potter and Neville Longbottom, making it an EitherOrProphecy. However, as [[SelfFulfillingProphecy Voldemort chose to go after him instead of Neville, Harry indeed became the boy the Prophecy was referring to, giving him the power to defeat Voldemort and the motivation to do so.]] The final lines of the prophecy state that Voldemort would "mark him as his equal", that Harry has powers that Voldemort does not know of, and that either Harry or Voldemort must kill the other.
A Death Eater eavesdropped and heard the first part of the prophecy, but was thrown out before he could hear those final lines. Thus Voldemort resolved to kill Harry, but did not realise the true danger that Harry posed to him. Since returning, he has spent months trying to find out the remainder of the prophecy. Dumbledore explains that the powers that Harry has that Voldemort does not know of are [[ThePowerOfLove his ability to love]]. This was why Voldemort's attempt to possess Harry failed in the previous chapter.