Quick Answer: Speculation from contexts suggests Cersei and Qyburn may be planning to use the late king Aerys Targaryen's stash of wildfire hidden beneath the Red Keep as a weapon to attack the Faith Militant and kill the High Sparrow. Doing so would be devastating to a portion of King's Landing, but would free Cersei of certain punishment should she be forced to stand trial before the Faith.

Cersei (Lena Headey) doubles her ferocity when stuck in an unwinnable situation. Her spacious life as a Lannister has filled her existence with privilege and immunity, and when she’s stuck in a corner, Game of Thrones (2011-) merciless mother knows no solution but to call on the resources at her disposal to attack those she feels are threatening her.

Typically, she lets others do the dirty work. That tendency was to continue during her trial with the Faith, with her champion The Mountain (Hafþór Júlíus Björnsson) as her certain victor in a trial by combat. That is, until her own son, King Tommen (Dean-Charles Chapman), decreed trial by combat illegal, outdated, and an ineffective punishment based on corrupt old practices that denied true repentance for crimes in the eyes of the gods.

“She might actually be screwed this time,” millions of television viewers likely said out loud upon hearing the decree. And so it seemed -- but only for a matter of seconds, as the announcement was followed by a brief exchange between Cersei and Qyburn (Anton Lesser) that lacked context and meant little at the moment, but could have big ramifications for Cersei’s future.

“That old rumor you told me about,” Qyburn said. “My little birds investigated.”
“Is it just a rumor or something more?” she asked.
“More. Much more.”

What was that? Vague. But it also let us know that, as always, Cersei has a plan. She’s not going to let the High Sparrow (Jonathan Pryce), a man she put into power, take her down -- no matter the cost. As she says earlier in the episode when tested by the Faith, "I choose violence."

Back in Episode Six of Season Six, “Blood of my Blood,” Bran Stark (Isaac Hempstead-Wright) witnessed a massive montage of scenes in one of his greensight visions:

Those shots of The Mad King shouting “burn them all!” while concoctions of green potion are mixed could have implications for the future. King Aerys was said to have had caches of wildfire created and stockpiled under King’s Landing during Robert’s Rebellion. (Thanks to the events of the Battle of Blackwater, we know what wildfire looks like, and it’s that same Ecto Cooler-colored liquid from Bran’s dreams.) Aerys’ plan was to burn King’s Landing to the ground, seeing as he thought he would pull a Targaryen and rise from the flames unscathed. Jaime (Nikolaj Coster-Waldeau) ended up stabbing him before any of that was possible, and the secret stash of wildfire remained hidden throughout the years. It seems Qyburn's "little birds" have found it, and could very well be what Cersei is referencing when she mentions “olc rumors." She wanted to know if the stockpile exists and if it is as big as legend reports.

Cersei is a woman out of options. If she goes to trial with the Faith, she’s almost certain to be doomed based on the reality of her crimes in the eyes of the church. A trial by combat won’t be possible, and given her impressive lack of loyalists and authority, neither would amassing the people necessary to launch a full-frontal assault on the Sept and its protectors. But Cersei is the last person in Game of Thrones willing to throw in the towel. Her scenes in “No One” are juxtaposed with ones of Jaime telling Edmure Tully (Tobias Menzies) about her strength as a mother. Jaime told Edmure of Cersei’s incredible passion, the same fiery vigilance by which Catelyn Stark (Michelle Fairley) loved her children, and how it is something that surpasses nature and rationale. And he tells Edmure he would “burn entire cities to the ground” for her. Cersei has made the same claim regarding her fortitude on numerous occasions throughout the series.

In the previous episode, Lady Olenna (Diana Rigg) chastised Cersei for her lack of support and doomed prospects. “You’re surrounded by enemies, thousands of them. Are you going to kill them all by yourself?” Olenna asks.

Perhaps. Is the exploding wildfire we see in Bran’s vision a look into the future, not the past? We know Aerys didn’t use it, so what were we witnessing? Even if Cersei doesn’t intend to level the whole of King’s Landing, she certainly has the resources to take out the Sept of Baelor and all those involved with the Faith.

Every time a Lannister mentions burning a city to the ground, it is in reference to protecting their children. Cersei was bestowed a prophecy as a child that said all her children would die before her (as well as suggesting she'll die at the hand of Tyrion or Jaime). With only one child left alive, she’s close, and her desire to prove that prophesy false and protect Tommen is immeasurable -- even when Tommen is responsible for the death sentence she otherwise faces. (Of course, he could always perish in the wildfire blast and Cersei could be responsible for the fulfillment of the prophecy she aims to stop.)

For extra consideration on this theory, we look back a few seasons. Back in the House of the Undying in Season Two, Daenerys (Emilia Clarke) experienced a vision in which she made her way to King’s Landing and entered the throne room, only to find it ruined and covered with flakes of either snow or ash, with the symbol of the seven perched above the throne. It may have no relevance, but maybe it does.


The throne room in Dany's vision

Whatever happens,  Season Six has reminded us exactly who the Lannisters are and why they are in contest with their opposing houses. It has refreshed the waning seriousness of Cersei’s loathsome personality and returned her to her typical, vengeful, horrendous self, and it has sown the seeds of some very big (and likely catastrophic) realities to come in the episodes and seasons ahead.