Quite literally, we saw these shots of Drogon flying over King's Landing from Bran's vision play out — but the more symbolic elements also revealed themselves.
The most significant part of the vision, in hindsight, is the way Dany and the birth of her dragons is connected with shots of her father screaming "burn them all."
The other vision that basically came true (and will likely be completed in the next episode) is what Dany saw in the House of the Undying back in Season 2.
In that vision, Dany was in a badly damaged throne room that appeared to be covered in snow — which many thought was foreshadowing Jon Snow's claim. It now seems like it was really ash, and it was showing us how Dany herself would destroy the Red Keep with Drogon.
In fact, it's extremely likely Dany is going to die in the next episode — as suggested by her vision itself. After turning away from the throne, she heads beyond the Wall and winds up in a tent where she meets Drogo and Rhaego. For a moment, she believes she's dead. Which is probably exactly what is going to happen next!
But! At least we know what those visions meant now!