For almost six seasons on Game of Thrones, we've seen Cersei Lannister willing to protect and uplift her children at literally any costs. After a childhood prophecy informed her that she's lose her three children, and considering she's down to only one left now, she is more desperate than ever to protect Tommen. Unfortunately, he just betrayed his mother in an unthinkable way, basically sentencing her to death. So will Cersei kill Tommen on Game of Thrones to save herself? Her cryptic side-convo with Maester Qyburn may be a reference to it.
Cersei finds herself epically screwed over by her son because she is still awaiting trial for her supposed crimes against The Faith of the Seven. That wasn't a huge problem for Cersei, since she and Qyburn successfully resurrected The Mountain into an undead warrior who is loyal to her. She planned on simply invoking a trial by combat with The Mountain representing her, like she has before, should a trial ever be set into motion by The High Sparrow. Unfortunately, to get her brother Loras out of the dungeons, Margaery Tyrell converts to religious fanaticism, converts Tommen, and convinces her husband the King to join The Crown and The Faith. Tommen essentially now controls the kingdom with religion, and, since The High Sparrow is his chief spiritual advisor, he agrees to outlaw trial by combat at first mention of it.
This leaves Cersei defenseless and sure to be condemned to death. So, she sends Qyburn to check on a "rumor" she's caught wind of and he confirms that the rumor is "much more" than they ever could have dreamed of. Speculation abounds that the rumor they're referring to is the fact that there is wildfire hidden all around King's Landing, leftover from Mad King Aerys' plot to burn down the city should anyone ever rebel against him. Unfortunately, Jaime slays the king before he can execute that plan and Bran's epic saga of a flashback contains some images of wildfire engulfing the castle, prompting some to wonder if that particular image was a flash-forward and not a flashback.
It's entirely possible, here, that Cersei will set off the wildfire reserves left in the castle, killing Tommen in the process, just to save herself. She and Jaime have been making "burn their cities to the ground" metaphors all season, and Dany has a vision in Season 2 of walking up to The Iron Throne in a room seemingly covered in ash. The good news is, there are only two episodes left in Season 6, so this set-up will play out very, very soon.