Harry Potter and the Prisoner of Azkaban

Further information: Plot of the novel
Harry Potter, now aged 13, has been spending another dissatisfying summer at Privet Drive. When Uncle Vernon's sister, Marge, insults Harry's parents, he becomes angry and accidentally causes her to inflate and float away. Harry flees with his luggage, fed up with his life with the Dursleys. The Knight Bus delivers Harry to the Leaky Cauldron, where he is forgiven by Minister of Magic Cornelius Fudge for using magic outside of Hogwarts. After reuniting with his best friends Ron and Hermione, Harry learns that Sirius Black, a convicted supporter of the dark wizard Voldemort, who murdered Harry's parents, has escaped Azkaban prison, intending to kill Harry.
The trio are returning to Hogwarts for the school year on the Hogwarts Express when dementors suddenly board the train, searching for Sirius. One enters the trio's compartment, causing Harry to pass out. New Defence Against the Dark Arts teacher Professor Lupin repels the dementor with a Patronus Charm. At Hogwarts, headmaster Albus Dumbledore announces that dementors will be guarding the school while Sirius is at large. Hogwarts groundskeeper Hagrid is announced as the new Care of Magical Creatures teacher; his first class goes awry when Draco Malfoy deliberately provokes a hippogriff, Buckbeak, who attacks him. Draco's father Lucius Malfoy later has Buckbeak sentenced to death.
The Fat Lady's portrait, which guards the Gryffindor quarters, is found ruined and empty. Terrified and hiding in another painting, the Fat Lady tells Dumbledore that Sirius Black has entered the castle. During a stormy Quidditch match, dementors attack Harry, causing him to fall off his broomstick, which is then destroyed by the Whomping Willow. Lupin privately teaches Harry to defend himself against dementors, using the Patronus Charm. At Hogsmeade, Harry is shocked to learn that not only had Sirius Black been his parents' best friend and betrayed them to Voldemort, but that Sirius is also his godfather.
After Harry, Ron and Hermione witness Buckbeak's execution, Ron's pet rat Scabbers bites him and escapes. When Ron gives chase, a large dog appears and drags both Ron and Scabbers into a hole at the Whomping Willow's base, which is actually an underground passage to the Shrieking Shack. The trio discovers that the dog is actually Sirius, who is an Animagus. Lupin arrives and embraces Sirius as an old friend. He admits to being a werewolf, and explains that Sirius is innocent. Sirius was falsely accused of betraying James and Lily to Voldemort, and murdering their mutual friend Peter Pettigrew. It is revealed that Scabbers is actually Pettigrew, an Animagus who committed the crime for which Sirius was convicted. After forcing him back into a human, Lupin and Sirius prepare to kill him, but Harry convinces them to turn Pettigrew over to the dementors.
As the group departs, the full moon rises; Lupin transforms into a werewolf, and Sirius transforms into his dog form to fight him off. In the chaos, Pettigrew escapes in his rat form. Sirius and Harry are attacked by dementors and Harry sees a figure in the distance save them by casting a powerful Patronus spell. He believes the mysterious figure is his dead father, and passes out. He awakens to discover that Sirius has been captured and sentenced to the Dementor's Kiss. Acting on Dumbledore's advice, Harry and Hermione travel back in time with Hermione's Time Turner, and watch themselves and Ron repeat the night's events. They save Buckbeak from execution and witness the Dementors overpower Sirius and Harry. The present Harry realises that it was actually him who conjured the Patronus, and does so again. Harry and Hermione then rescue Sirius, who escapes on Buckbeak. Lupin resigns to preempt an uproar from parents over a werewolf teaching their children. Sirius sends Harry a Firebolt broom, the fastest broom in the world, and Harry happily takes it for a ride.

Question: Harry was forgiven, what for?
Answer: for using magic outside of Hogwarts