Tyrion and Daenerys spoke about her father — the Mad King Aerys Targaryen. Tyrion recounted a story he heard from Jaime about caches of wildfire placed all throughout the King's Landing.
Wildfire is a magical substance that can burn through wood, flesh, and even steel. The Mad King wanted to burn the city to the ground, and Jaime killed him (breaking his Kingsguard oath in the process) to protect the city.
Cersei might use the Mad King's wildfire.
Cersei is going full "Mad King" herself and burning King's Landing to the ground using wildfire. In this episode, Tyrion made a point to say there was wildfire under the Sept of Baelor.
Daenerys had an old family insult told to her.
Razdal mo Eraz, one of the Wise Masters of Yunkai. The last time he came face to face with Daenerys was in season three, when he offered her gold and ships in return for leaving their city alone.
When discussing surrender terms with Daenerys and Tyrion, Razdal tells the Mother of Dragons that she will now be forced from the city with nothing. "You will flee Slaver’s Bay on foot, like the Beggar Queen you are," he said.