James and Lily Potter
The Potters, of course, only appear in flashback form or in passing conversation. They are, after all, dead. And it's their death that really drives not just this book, but the entire series. Harry wouldn't be who he is if his parents were alive, and in many ways his entire life is bound up in the fact that they are dead. It's the how part of their death that's really crucial, though. And that has some double meaning, so let's explain.
The answer to how the Potters died is that Voldemort killed them. And this is a crucial detail since it has everything to do with Harry's own ongoing war against Voldemort and the threat he poses. But there's another part of the how, and that is in what manner the Potters died. We get that answered here thanks to the Dementors, who act as a sort of antenna for bad memories and traumatic flashbacks. When Harry is around them, he hears his parents' death playing in his head like a monstrous radio program. And in hearing his parents die, Harry learned more about how they lived than he ever had before. We learn that James faced off alone against Voldemort, in an effort to save his family. And we learn that Lily pleaded with her killer in an effort to save her son's life. The sacrifice that Harry's parents made becomes a lot more tangible here and Harry has a real struggle with these new revelations and with his own unresolved feelings about his parents.
We also learn some lighter facts about James in this book, namely through the Marauder's Map. James and his BFF Sirius sounded like the Fred and George Weasley of yore. But Harry's dad wasn't just a jokester – he was also a decent guy who tried to help his friend Remus get through his difficult werewolf transformations and who saved Snape from a dangerous joke that his reckless friend Sirius set up. It's fitting that Harry was able to really connect with his dad through his Patronus – James sounds like the type of person who would make a great guardian spirit. We still know comparatively little about Lily's life at Hogwarts or her friends, but Harry forges a very strong emotional connection with his mother via the Dementor-induced flashbacks.