Daenerys contends with her family's history in Westeros. The Targaryens united the Seven Kingdoms under the Iron Throne using the force of dragons. Remember: that iconic Throne was constructed from the melted down blades of those who opposed them. Then, of course, there's her father the Mad King, who doesn't have a great reputation beyond Ser Barristan Selmy (RIP). That's why she decides against becoming what Tyrion and Varys say will be a "Queen of Ashes." The alternate plan: her Westerosi soldiers will lay siege to King's Landing while her foreign faction devastates House Lannister by attacking their ancestral fortress, Casterly Rock
The most interesting twist on the Targaryen story this week: Melisandre shows up at Dragonstone (where she previously burned people alive and took sexually intimidating baths) to let the gang know that Daenerys might be the "Prince Who Was Promised" a.k.a. Azor Ahai incarnate! He's a Beowulf-like hero endorsed by the Lord of Light, and if you want more on what exactly that theory is and means for the rest of the series, you'll need this full-on explainer.
Apparently the prophecy is genderless, although Melisandre isn't clear at this point if Jon Snow or Daenerys is the Prince she's been searching for, only that the bastard son of Ned Stark plays a pivotal role in this tapestry of conquest. Missandei's translation corner aside, the nature of the Azor Ahai prophecy continues to be vague. Melisandre doesn't totally trust the prophecy, but she tells Dany and Tyrion to at least recognize Jon Snow as a powerful ally, which he will become, next week... when he finally gets to Dragonstone.
Some of the early Targaryen planning sessions seem to be moot, though, given the events at the end of the episode. With the rebel Greyjoys and the Sand Snakes apparently unable to take King's Landing after the Tyrells take on Casterly Rock, strategies might have to shift. Or, maybe a grand entrance under the threat of being the "Queen of Ashes" can go a long way. Let the Dothraki loose on one city, because why not?