House of the Dragon is set roughly 200 years before the events of Game of Thrones. As such, the Game of Thrones characters know the history of House of the Dragon, understanding what caused the infamous Dance of Dragons civil war, who ended up victorious, and what it cost House Targaryen.
Usually, this amounts to a few fun Easter eggs or name drops here and there, with occasional references to Rhaenyra Targaryen (Emma D'Arcy) and her half brother Aegon (Tom Glynn-Carney) finding themselves recontextualized after audiences had the opportunity to meet those characters in House of the Dragon. However, in one instance, the actual story of House of the Dragon plays a key role in Game of Thrones, acting as a warning for an important figure from Thrones, which he promptly ignores.

Stannis sacrifices Shireen
In Game of Thrones season 5, Stannis Baratheon (Stephen Dillane) infamously sacrifices his daughter, Shireen (Kerry Ingram), burning her at the stake at the insistence of Melisandre (Carice van Houten) to appease the Lord of Light. Melisandre has previously demonstrated the power of king's blood after collecting some samples from Gendry (Joe Dempsie), the bastard son of King Robert Baratheon (Mark Addy), Stannis' brother. When she burned leeches containing Gendry's blood, Stannis' rival kings died shortly thereafter, cementing his faith in her power.
In burning Shireen, Stannis had hoped to secure victory against the Boltons from the Lord of Light. However, this backfires, and the Bolton army easily dispatches Stannis' starving men. Stannis himself is grievously injured during the battle. When he encounters a vengeance-seeking Brienne of Tarth (Gwendoline Christie) amid the carnage, knowing he murdered his only daughter for nothing, he simply lets her kill him, realizing that the Iron Throne is no longer within his reach.

Stannis could have learned from the Targaryens' mistakes
Stannis could have avoided his downfall simply by listening to Shireen's story. When he first approaches her to ask if she can help him "fulfill his destiny," Shireen is reading a book, which she explains is the history of the Dance of Dragons, the events depicted in House of the Dragon. Shireen tells her father the story of the Targaryen civil war, essentially spoiling the ending of House of the Dragon over a decade before it would air.
In addition to the damage done to Westeros, Shireen emphasizes that the Dance of Dragons ruined the Targaryens themselves. Their infighting resulted in the deaths of countless family members, as well as the eventual demise of the noble house's iconic dragons, the source of their power and fear factor. Shireen, even as a young girl, understands how the Dance weakened the Targaryens' control over Westeros and led to Robert's Rebellion nearly two centuries later.
Kinslaying is considered among the worst taboos in all of Westeros, which Shireen emphasizes in telling the story to Stannis. This makes sense, given the importance the role of family plays in typical Westerosi customs. This is part of the burden Tyrion (Peter Dinklage) carries throughout the later half of the series, after being falsely accused of killing his nephew Joffrey (Jack Gleason) before actually murdering his father, Tywin (Charles Dance). Kinslayers are also said to be cursed, as Rickard Karstark (John Stahl) reminds his distant cousin, Robb Stark (Richard Madden), shortly before his execution. To prove Rickard's point further, Robb dies shortly thereafter at the dreaded Red Wedding. Perhaps the decline of House Targaryen after its members fought and killed each other helped to further popularize this myth.
When Shireen reminds Stannis of the importance of the family unit both in Westerosi traditions and superstitions, Stannis immediately doubles down on kinslaying and murders his daughter. He failed to learn from the mistakes of past rulers of Westeros, instead overly relying on Melisandre's unpredictable, invisible magic, paying far too great a price in the process.

Additionally, Stannis had already killed a member of his family. Though it is never entirely clear if he knows the role he plays in the death of Renly Baratheon (Gethin Anthony), his younger brother and rival for the Iron Throne, Stannis helped Melisandre create the demon that snuck into Renly's camp and stabbed him to death, with Brienne taking the blame. This adds extra symbolism to the fact that the woman who suffered from Stannis' first act of kinslaying kills him not long after his second.
Most Westerosi historians agree that the Dance of Dragons was ultimately inevitable, set in motion by King Viserys Targaryen's (Paddy Considine) mistakes. However, Stannis' own demise was entirely avoidable. If he had listened to Shireen's story, and common sense, he would not have burned her, and wouldn't have led his army into a battle they couldn't have possibly won riding on blind faith in the Lord of Light. Stannis' failure to learn from history when Shireen reads it directly to him showcases that he probably wasn't the best fit to rule the Seven Kingdoms after all.
For more from the world of Westeros, make sure to stream House of the Dragon season 3 on HBO Max.
