Daenerys Targaryen suffered one blow after another on Game of Thrones after finally coming ashore in Westeros. Her dragon Viserion became a tool of the White Walkers; her loyal supporter Jorah was killed in battle; lastly, her new boyfriend turned out to be her nephew. Then when traveling to King's Landing, yet another tragedy befell her: a second dragon died on Game of Thrones, and no one is OK with that. Least of all Dany.
The moment itself came as a shock. While Daenerys' fleet sailed towards King's Landing, she rode above on Drogon with Rhaegal accompanying them. Then, out of nowhere, gigantic arrows began flying through the air. Rhaegal was impaled through the throat, wing, and body; he took so many hits that it was clear there was no coming back. Eventually he fell from the sky and was submerged beneath the waves.
Euron's bevy of ships came into view with the huge crossbow that Qyburn had previously devised to take out the dragons. He managed to not only murder one of Daenerys' children, but to destroy her ships and kidnap Missandei. At this point, I can only assume that Dany regrets ever arriving in Westeros. She could still be in Essos, enjoying the warmth and sunshine with three whole dragons and no boyfriend-nephews. Surely that would be preferable!
Daenerys spent much of her adult life fixated on conquering the Iron Throne because she felt it was her birthright. Her family had ruled for centuries until they were driven out of the country, and she wanted to return to the place that was supposed to be her home. But she's faced numerous setbacks even as she inches closer and closer to her goal. Her armies have been decimated and her friends killed; her advisors are losing faith in her and Jon Snow is now a genuine threat to her claim on the throne. Even when she had nothing else, she had her dragons, and they're nearly gone, too.
Daenerys was able to amass so much power because of her dragons. When the options were to do what she said or become tasty barbecue, most people chose the former. That was (in part) what allowed her to form such impressive armies and take so many cities. She loved her dragons like they were her children, but they were also her most effective weapon. And while one dragon is nothing to sneeze at, it's still quite a step back from three.
Drogon is the only dragon who remains. And that makes him all the more precious; if Daenerys loses him too, then she'll truly be at her lowest point. Her dragons seemed indestructible for so long, but her enemies have figured out how to beat them. Dany will have to risk Drogon's life in order to fight back against Cersei. If she chooses to keep him out of the fray, he might be safe, but she'll be severely weakened.
Rhaegal's death (and the subsequent execution of Missandei) is a turning point for Daenerys. After losing so much, there's no telling what she'll do now.