Dany visits the House of the Undying, a large ancient structure in ruin.
Pyat Pree greets Dany at the entrance and gives her instructions for passing through the interior's labyrinth. He also has her drink a drug called shade of the evening. Basically, Pyat is the Timothy Leary of Essos.
Dany enters the derelict interior with Drogon.
Within, she sees several visions of the past and the future; among them are a dead man with a wolf's head and an iron crown, her childhood home in Braavos, and a Targaryen man proclaiming his son's song shall be the song of ice and fire.
She comes to a great hall where beautifully dressed wizards and kings claim to have waited for her a thousand years and sent the comet to show her the way.
Doubting the image, she follows Drogon to another door and discovers the Undying behind it, all ancient, mummified corpses.
The Undying prophesy Dany's future, and the images center on the number three (three trials, three mounts, three reasons).
Dany has several more visions before the Undying attack her. Drogon saves her with his fire breath—thousand-year-old bodies are, it seems, highly flammable.
Dany and Drogon push their way outside of the House of the Undying. Pyat rushes at her, knife drawn, but Jhogo stops the warlock with his whip.