A destructive backstory
Several times throughout the series, the Starks and Lannisters mention the Mad King burning people alive. As the series progressed, we've learned more about wildfire and it's destructive properties, but the show's dialogue doesn't shoot straight about Aerys II Targaryen actually burning Ned Stark's father, Rickard, to death or that he had his brother Brandon strangled. On the show, a lot of references are made of Robert Baratheon starting "Robert's Rebellion" to save Lyanna Stark, Ned's sister, but little direct dialogue references that the Starks joined the Baratheons in the Rebellion after the former Warden of the North was burned alive.
The twisted story of Lyanna Stark
The story of Lyanna is first introduced in the pilot when King Robert visits the crypts of Winterfell, and is later repeated in the Season 5 with Sansa and Littlefinger in that same crypt, just before we learn what we've known is a lie. In the first season, the important thing that we know is that Rhaegar Targaryen, son of the Mad King, stole Lyanna (Ned's sister and Robert's betrothed), and raped her to death, kicking off the rebellion that put Robert on the throne. Naturally, that story is almost entirely false, but there's only a few hints in the first season that this isn't what happened. Most of interest is a scene between Ned and Robert on the Kingsroad back to King's Landing where Robert tries to get Ned to discuss Jon Snow's mother and Ned has to avoid talking about his sister.