Firstly, Jon Snow dying will secure her right to the throne since we know he's Aegon Targaryen - a fact that Sansa, Arya, Tyrion and Lord Varys know. When Jon arrived in Dragonstone, Varys tried to convince him that he would be the better ruler. She says Jon Snow, while Tyrion says Varys. Dany wants to be queen but she's not leaving many subjects in the capital to be ruled over.
Varys is taken from his chambers and executed for treason. She was crushed in the tunnels beneath King's Landing after Dany went full-DRACARYS on everything and everyone. The armies have indeed traveled south to King's Landing, taking no time for R&R other than one drunken night in a tavern that apparently serves fresh-brewed Starbucks. Or how about the time he told Danerys to trust Cersei and that she'd be sending her army to help? Eventually, Jon ordered his troops to fall back. Tyrion's obsession with saving 10,000 innocent lives was so wise and noble, but his continued trust of Dany, his belief that she would honor the ringing bells despite her insane eyes and pouty face, was not. Arya wisely took his advice and began to paw her way through the terrified throng. She found a horse and rode it away.
Inside the Red Keep, Arya and the Hound made it to the Map Room. Next up, Qyburn dies in 3 seconds, with only a push from Ser Gregor aka The Mountain.
We also got to see The Mountain out of his suit of armour and to be fair it was terrifying. Near the bottom they encountered the Hound who had come for his brother. When that didn't work, Sandor threw himself and his brother from a tower and into the smoldering dragon fire below. At first Jaime resists, but Tyrion gives him a plan that, if it all works, would allow him to start a new life with Cersei. As Daenerys's Hand, Tyrion gained access to him and set him free.
Unfortunately, Jaime missed the cutoff as the gates to the Red Keep closed, so he had to find another way in. It allowed her to surprise Euron Greyjoy (Pilou Asbaek) and his Iron Fleet. Despite Jaime ultimately besting him, Euron rejoiced at having killed Jaime, who wasn't dead yet. Euron dies staring at the sky yelling, "I'm the man who killed Jaime Lannister".
Cersei and Jaime are reunited on the map where he left her, and she cries in his arms. In the end, they went out in a blaze of glory, falling out one of the open arches and into the flames below, locked in a grisly embrace.
Arya survived the episode, but Jaime and Cersei did not - in a move that was also destined from the beginning of the series.