Everyone around Tyrion mocks and despises him, predominantly because he is unusually short and odd looking. His father is notably dismissive and favors his other children over Tyrion. In response, Tyrion is sarcastic and moody, and he engages in misbehavior like drinking too much and routinely hiring prostitutes. Indeed, as we have learned in the earlier novels, Tyrion believes he married one such prostitute, Tysha, and the aftermath of that event had a profound effect on Tyrion that influences his present behavior. Tyrion met Tysha when he and Jaime came across some men assaulting her, and they drove the men off. Tyrion fell in love with her and married her, but Tywin disapproved, and as punishment had his soldiers rape Tysha in front of Tyrion. His brother Jaime told Tyrion that Tysha was a prostitute all along and they’d planned the whole episode so Tyrion could lose his virginity. Now, Tyrion still despises and distrusts his father, and he often does things just to spite him. He distrusts Jaime as well. The event also made Tyrion skeptical that any woman could genuinely love him, which is a large part of the reason that Tyrion prefers dealing with prostitutes to women at the court. (Of course we learn at the end of the novel that Tysha wasn’t really a prostitute and Jaime lied.) For all these reasons, Tyrion is a constant outsider, despite being among the most intelligent and capable characters in the series.
By the end of the novel, however, Tyrion has changed from resigned outsider among the Lannisters to a hateful enemy of his family. In the previous book, Tyrion showed great cunning and courage in battle, and his efforts helped save King's Landing and the Lannister family. But despite his bravery and tenacity, no one in his family shows him any respect or gratitude. Tyrion feels further alienated as his father and sister heap constant abuse on him. When he is accused of Joffrey's murder and imprisoned, he isn't exactly surprised, but he nonetheless feels extraordinarily betrayed, as he had worked only for the good of his family. Aggravating that sense of betrayal is Shae's abandonment of Tyrion, which recalls for him his experience with Tysha. These feelings of betrayal boil over with Jaime's revelation that Tysha did truly love him. She wasn't with him for money but because she wanted to be, and yet his father, with no resistance from Jaime, had her brutally raped to teach Tyrion a lesson. Before Tyrion flees, he vows revenge on Jaime, then seeks his father out. Finding Shae in his bedroom, he murders her first, then his father, getting his vengeance against both.
In many ways, Jaime has played the classic villain in the series to this point. He is violent, verbally abusive, and cares little for the people around him, in fact seems willing to casually murder them if it suits him. His incestuous relationship with his twin sister Cersei adds to his loathsomeness. But he undergoes a radical transition over the course of this novel as he struggles to recapture his sense of honor. Brienne of Tarth plays a significant role in this transition. As she escorts Jaime to King's Landing, she repeatedly confounds Jaime's expectations of her. She maintains her composure through his abuse, proves herself an excellent fighter (practically Jaime's equal, in fact), never once waivers from her oath to Catelyn Stark, and embodies all the virtues of knighthood. What makes all this so extraordinary to Jaime is that Brienne is a woman, and so she defies every convention Jaime knows and every prejudice Jaime feels about women. Previously he had valued them mostly for appearance, but the unattractive Brienne proves valuable for very different reasons. Jaime comes to genuinely respect her, and ultimately to care for her, evidenced by his saving her from the bear pit.
The effects on Jaime are twofold: First, through her actions Brienne reminds him what honor is and suggests to Jaime that he need not conform to what anyone expects of him. Though he is considered despicable by many, for killing King Aerys among other reasons, he doesn't have to fulfill that expectation. Second, she seems to reveal to Jaime, or at least prompt him to see, what a terrible person Cersei is. When Jaime comes back in contact with Cersei after spending most of the novel with Brienne, he quickly has a change of heart about his sister and sees what a vain, selfish, and deceitful person she is. She is, in essence, the opposite of Brienne: valuable primarily for her appearance and little else.
Along with Brienne, Jaime's loss of his hand is the other main catalyst in his change. His sense of identity and value of himself was tied directly to his prowess as a swordsman. With that taken from him, he undergoes an identity crisis and begins to wonder what value, if any, he has left. This crisis continues as, back at King's Landing, he reads the stories of the knights of the Kingsguard in the White Book. He thinks of his own history, including his killing of King Aerys Targaryen, and doesn't like what it says of him. At that point he seems to recognize that his value was not contained in his sword hand, that even before that loss he may not have possessed the value he thought. To change his story as it will be written in the White Book, he makes an effort to act as he thinks is honorable and right. He even tries to make amends for past misdeeds, as when he frees Tyrion and reveals to him the truth about Tysha.
In the first book of the series, Daenerys was timid and unsure of herself. Now, with three dragons and a band of loyal followers, Daenerys has become a strong and spirited leader, and in this novel she continues to grow bolder as she adds liberator and conqueror to her titles. Her feelings of disgust and revulsion toward slavery, and her empathy for and desire to protect the slaves, prompt much of her behavior in the novel. She initially goes to Slaver's Bay to buy an army of slaves so she can retake Westeros, but her plans change as she sees how the slaves are treated. Her original intent of finding an army becomes a mission to free the enslaved men and women in the region. Once they're free, she feels obligated to care for them, and she becomes a maternal savior figure to the freed slaves. She even begins referring to them as her “children.” The role is notable because, where in the first novel of the series Daenerys felt completely helpless, she now feels she is strong enough to act as caretaker for legions of men, women, and children. Beyond just empathy, her behavior demonstrates a great deal of self-assurance. Clearly she feels not only capable but powerful as she and her new army march lastly on Meereen.
Daenerys's actions also stand her in direct contrast to the rulers we've seen in Westeros, suggesting she might possibly be the best choice to rule Westeros. Thus far in the series, two kings have sat the Iron Throne: Robert Baratheon, who spent a great deal of his time drunk and cared little for the actual duties of ruling; and Joffrey Lannister, who is cruel, arrogant, and immature. Moreover, we've heard stories about the king that Robert Baratheon replaced: Aerys Targaryen, who was Daenerys's own father. Known as the Mad King, he was arguably insane and definitely brutal, given to roasting his enemies alive. Daenerys, on the other hand, comes across as reasonable, kind, and genuinely concerned with the well-being of those she leads, making her potentially an ideal ruler.
The great challenges Jon faces in the novel are ones of identity, and after struggling to navigate these challenges he finally comes into a role he feels comfortable in. As he is frequently reminded, Jon is a bastard. He grew up with the Stark family, but he was never fully one of them, and the subsidiary role he played made him feel like a permanent outsider. When the novel begins, Jon is again an outsider. He pretends to join the wildlings but is actually still committed to the Night's Watch. But his time with the wildlings complicates his sense of where he belongs. To his great surprise, he finds that he fits in to a degree with the wildlings, who are themselves all outsiders in a sense living beyond the rule of the Iron Throne, and he genuinely likes a number of them. More troubling, he falls in love with Ygritte, a wildling woman. As a member of the Watch, he took a vow to forsake such relationships, but he eventually breaks his vow and carries on a romantic affair with her. John is left feeling torn between his loyalty to the Watch and his love for Ygritte and sympathy for the wildlings, but since they're marching to attack The Wall, he knows he will have to choose a side. He can remain with the wildlings and take on a new identity as one of them, or he can return to the Watch. Ultimately Jon escapse from the wildlings and informs the Watch of their intent to attack, but he still harbors feelings for Ygritte and sees the wildlings differently than he did before.
Jon later faces perhaps a more difficult decision after Stannis arrives and offers him rule of Winterfell. Growing up, Jon wanted desperately to be acknowledged as a Stark, but because he was a bastard, he was never considered a full member of the family. As a consequence he would also never be able to inherit Winterfell, even though he was the second oldest of the Stark children. Jon's status in his family was one of the motivating forces behind him joining the Night's Watch. It offered him basically a new family where he was equal to his brothers. Though he had some conflicts and didn't always get along with his new brothers, Jon was still able to make a place among them. Gradually he has shown himself a leader in the Watch, and during the battle with the wildlings, Jon demonstrates his ability in that role and wins yet more respect from his brothers. It's enough that, with a little clever strategizing from Sam, he is chosen their new Lord Commander. When Stannis offers Jon Winterfell, and the position he always dreamed of, he is essentially forced to choose an identity. He can be a Stark or a member of the Night's Watch. But as Jon weighs the decision, he recognizes that ruling Winterfell won't suddenly make him more of a Stark. He sees what he has found in the Night's Watch, and his decision to stay and serve as Lord Commander shows that he feels he has finally found his place and his identity there.
Having witnessed a great deal of death and cruelty for her age, Arya is filled with rage. When her thoughts are not focused on survival, they generally turn to her desire for revenge against the people who have hurt her family and friends. She is also trying desperately to take control of her life despite being repeatedly taken captive by adults. Because she is still young and small, she's not able to fend for herself, and though she would prefer to fight her enemies like a wolf, she instead often has to hide like a mouse. Even so, Arya has already demonstrated a willingness to kill, and she doesn't feel any sense of remorse when she does. On the contrary, she wants to become more skilled at it. Her behavior suggests that killing seems quite normal to her, a fact that's hardly surprising given the tremendous amount of murder and death she's witnessed.