The odd thing is that the dream is from the point of view of the thing in the chair.
Suddenly, it occurs to Harry that the dream is from Lord Voldemort (Harry's nemesis) and that Voldemort is plotting to kill Harry (as usual).
Harry is stuck at Privet Drive for the summer break.
Privet Drive is where his incredibly unloving aunt (Petunia), uncle (Vernon), and cousin (Dudley) live.
Harry has to stay with them because, the same night that Voldemort tried and failed to kill Harry, he succeeded in murdering Harry's parents, Lily and James Potter.
So Harry stays with his mother's sister Petunia during summer holidays.
As proof of how horrible the Dursleys are, they "explained away Harry's long absences at Hogwarts School of Witchcraft and Wizardry over the previous three years by telling everyone that he went to St. Brutus's Secure Center for Incurably Criminal Boys" (2.15).
Harry thinks about who he might tell about his burning scar and his bad dreams.
Hermione Granger, one of his two best friends?
No, she'll just tell him to go to Professor Dumbledore. And then she'll throw some schoolbooks at him so that Harry can read up on curse scars.
Professor Dumbledore, his mentor at Hogwarts?
No! Harry would feel too stupid bothering Professor Dumbledore with something this small.
His other best friend, Ron Weasley?
No, he'll just freak out and ask his dad about it, and Harry doesn't want to bother Mr. Weasley either.
So Harry decides to write to Sirius Black.
Sirius Black is Harry's godfather. He's on the run for murdering Wormtail (Voldemort's assistant from the first chapter) but, of course, he didn't do it.
But Sirius can still get mail delivered by Harry's trusty owl, Hedwig.
So Harry writes Sirius a letter asking if "curse scars sometimes hurt years afterward?" (2.39).