Tyrion Lannister has suffered multiple indignities throughout the history of Game of Thrones, largely at the hands of his unfeeling father and fratricidal sister. In "The Laws of Gods and Men," they were paraded before him in a show trial, a series of lies, insults, and indignities, the kind he had been able to tolerate individually over the year but could not stand any more. Much like episode two, which spent half its running time on Joffrey's wedding, much of episode six was given over to Tyrion's trial. It was a bigger challenge, since Joffrey's wedding ended with his satisfying death, and this just had the cliffhanger of potential trial by combat. But it was charting an equally colossal moment.
"The Laws of Gods and Men" is a somewhat mocking title, considering the ridiculous nature of Tyrion's trial (he's given very little chance to defend himself or cross-examine witnesses), but it also refers to the laws that have long bound Tyrion to his noble family and served to protect him. Tywin once told him he would have happily left him to die but for the Lannister name Tyrion bears, and it's a name he's used to survive and thrive in a world that would have otherwise rejected him because of his stature. For all of his self-awareness, Tyrion has always considered himself a Lannister. In terms of his cunning and forward thinking, he's his father's truest heir, and as he reminded everyone in the throne room, he protected King's Landing from certain capture at the Blackwater.
Tyrion can shoulder the accusations leveled at him from people he despises (like Grand Maester Pycelle and Meryn Trant) and even from those he respects (Varys' testimony clearly stung, but Tyrion knows that Varys looks out for himself above anyone else). Just as with Ned's imprisonment in season one, we're led to believe that Tyrion will take the black and ride to the Wall, as part of a deal between Jaime and Tywin that will see Jaime become the heir his father wants him to be.
Just as with Ned, it all falls to pieces, with Shae's surprise testimony pushing Tyrion over the edge. He condemns the city's citizens, its court, and his father, tells his sister he's glad Joffrey died in front of her. Tyrion is exiting the family. The speech was a big Emmy moment for Peter Dinklage (a three-time nominee and one-time winner); undoubtedly stagey and necessarily grand, but vital as a turning point in Tyrion's relationship with his family. He's done scheming and playing his father's game, and now he just wants to leave it to the gods.
Another big "leaving the family" moment came earlier in the episode among the equally fraught Greyjoys. Feeling for her annoying younger brother ever since she saw his junk in a box, Yara has assembled a crack team of warriors to try and re-take him from Ramsay Snow. It's lovely to see Yara again, by the way—much more than her brother (who was raised in relative comfort in Winterfell), she represents the real salty grit the Ironborn are supposed to display, and more than her lame grumpy dad, she's trying to save the family honor by rescuing Theon. But once she sees the shrieking Reek in his cage, she knows he's pretty much gone forever. A lovely tying-off of that dangling storyline from season three; now Yara can hopefully move on to more interesting targets.
Everything else continues to trundle along at a slower pace as we gear up for the final arc of the season (there's only, sob, four episodes to go this year). Stannis' visit to the Iron Bank of Braavos was only slightly more exciting than a regular visit to the bank. He's literally just asking for a big loan, one to fight a war with, but given that he's Stannis, he's a little touchy about, y'know, asking for things he thinks he deserves by those pesky Laws of Gods and Men. Davos manages to speak up enough to figure it out, though, pointing out to banker Tycho (a suitably stone-faced Mark Gatiss) how thin the Lannister alliance keeping Westeros together really is.
It's notable just how many freakin' times the full title of the King of Westeros (King of the Andals and the First Men, Lord of the Seven Kingdoms, Protector of the Realm) was mentioned last night. Everyone adheres to all this procedure and ceremony to reinforce their various claims on power. Even Daenerys, receiving supplicants in her mighty new pyramid, has come up with an endless series of titles to terrify every potential friend or enemy with. But as we see, she has just as tenuous a grasp on things as anyone else. Her dragons are stealing goats from peasants and eating them alive, and the nobility of Meereen, at least some of whom she'll need on her side to keep things in order, are not going to quickly forget her mass crucifixions.
As Hizdahr zo Loraq (the plaintive nobleman who petitioned Daenerys for mercy) pointed out, there is a spectrum to everything, and her desire to solve things quickly and justly will just leave complicated results in her wake. This is Game of Thrones. Nothing can be done simply, and the plans pretty much every character makes always get dashed one way or another, whether or not they adhere to the rule of law and the codes of honor.