One of the many questions Game of Thrones fans still have in mind is what made Daenerys so unique that she could bond with—or at least, command—three dragons, knowing a rider can only mount one at a time.
From what we’ve seen in House of the Dragon, the feral beasts are very selective of who they want to be bonded with. A Targaryen can claim one, but it’s the dragon who chooses its rider.
Redditor explains why Daenerys can bond with three dragons in Game of Thrones

Daenerys Targaryen shared a special bond with her three dragons in Game of Thrones. She was initially gifted with three petrified dragon eggs, and she’s the first recorded Targaryen to hatch more than one. It’s important to note that they didn’t hatch by themselves. They needed a bit of blood magic and a funeral pyre to finish the job.
From their birth to growing into full-fledged dragons, Drogon, Rhaegal, and Viserion had a special connection with Dany. She can lead and command all three of them during battles, even though her bond is officially with Drogon.
A fan on Reddit shared an interesting theory about how Dany could “bond” with three dragons when in the prequel series, House of the Dragon, the Blacks had to hire dragonseeds because none of the legitimate members could command more than one.
As the user explained, Dany’s connection with her dragons goes beyond the blood that runs in her veins. There is a magical element that awakened as soon as she brought the dragons back to life. When the last dragon died, the magic in the world also vanished. These descendants of Valyria and their dragons possess a natural magical affinity to each other.
The netizen also claimed that the reason Dany managed to hatch three eggs is because she is The Prince That Was Promised. “She’s Aegon the Conqueror come again,” the fan noted. But, more importantly, she possessed a unique, almost supernatural bond with all three of them that they knew which ones to protect and which ones to attack during battles.
Another interesting point the fan mentioned is that there is a different bond that goes beyond natural imprinting.
House of the Dragon gives more depth to Daenerys’ bond with her dragons

Bonding with dragons is much more difficult in House of the Dragon. We’ve seen Seasmoke burn Ser Steffon Darklyn. We’ve witnessed the dragonseeds run for their lives as Vermithor spewed out dragonfire. If Rhaenyra could command and bond with more than one dragon, then all her problems would be solved.
What’s great about this contrast is how the prequel series highlights Dany’s relationship with her dragons. The challenges that her ancestors faced in the past add a new layer to her link with her three children. As mentioned, it’s more than just being a Targaryen—the birth of her dragons was magical, which gave her exceptional ability to bond with three of them, and it’s the same reason she’s immune to fire.