Each house has its own official mottos and unofficial sayings, which embody the family's character, and numerous slogans, sayings and jokes surface throughout the story as characters remind themselves of their background and duties. For example, the “words” of the House of Lannister, “Hear Me Roar!”, play on the family sigil, which is a lion. But there is a recurring mantra that “a Lannister always pays his debts,” and that saying is the one that more adequately sums up the Lannister family and its members. It suggests of course the vast wealth the Lannisters possess, but the “debts” it refers to aren't strictly financial. It also refers more ominously to the Lannisters' guarantee that they will avenge any wrongs done against them, and so the words serve as a reminder to everyone that the Lannisters are not to be crossed. The Stark motto, “Winter is coming,” also acts as a warning, but of a different type. In the world of the novel, winter may last a decade, and this brutal time is guaranteed to happen as it is simply a regular part of the cycle of seasons. The Starks, being among the northernmost families, endure the harshest winters, and the words indeed remind them to be prepared for winter. But they also function more broadly as a warning that one should always be prepared for trouble in any form.
The people of Westeros are familiar with a variety of songs, and they often hire minstrels to perform them. Some songs, like “The Bear and the Maiden Fair,” come up several times and in different contexts. Many of these songs are bawdy, others tell stories or recall moments in history, and generally act as a way to disseminate ideas and provide entertainment in a world without any kind of mass communication. Often, they also serve a functional or symbolic purpose in the plot. Olenna Redwyne, the “Queen of Thorns,” has her jester play very loudly in one instance so that the women’s conversation can't be overheard. In another scene, Samwell sings a song to comfort Gilly and remembers that his harsh father forbade the song because it sounded too soft and sweet, qualities his father also detested in him.
Numerous betrayals occur in the novel, and these betrayals often serve as turning points in the plot. Walder Frey feels betrayed by Robb’s decision to marry Jeyne Westerling rather than one of his daughters, which in turn leads him to plot his own betrayal. He ultimately conspires to have Robb, Catelyn, and many of the Stark bannermen murdered at what becomes known as the Red Wedding. Petyr Baelish, who has done a great deal for the Lannisters and been amply rewarded, betrays the Lannisters, unbeknownst to them, by planning Joffrey’s death by poison at his wedding. Shae betrays Tyrion by making false or exaggerated statements against him at his trial, prompting him to seek out a trial by combat. Additionally, Daenerys feels Ser Jorah and Barristan Selmy have both betrayed her by their dishonesty, and Daenerys is so hurt by Ser Jorah’s betrayal that she ultimately banishes him.
The sword Oathkeeper represents honor. It was forged from Eddard Stark’s greatsword, Ice, after it was used to behead Eddard at the order of Joffrey Lannister, and it was given to Jaime by Tywin when Jaime returned to King’s Landing. Ice had been in the Stark family for generations, and so it was an insult to the honor of the Stark family that the Lannisters, after killing Eddard, would melt it down. But Jaime changes the sword’s connotation when he names it Oathkeeper and gives it to Brienne. In essence, Jaime gives Brienne an instrument to carry out her vow to Catelyn Stark that she would find and return Catelyn's daughters. Jaime at the same time upholds his promise to Catelyn that he would send her daughters back if he were returned safely home. In the novel, honor is intrinsically tied to keeping one's oaths and doing what is morally correct, and so the act restores Jaime's honor and allows Brienne to uphold hers. The act also removes the sword's connotation of insult to the Starks as it is now a tool intended to help the Stark girls, so it restores the sword's honor in a sense as well. In these various ways the sword becomes a symbol of honorable behavior.
On the one hand, the Wall is a simple defense against the wildlings, but the Wall also acts as a figurative boundary between the natural and supernatural. The Wall exists as a literal defense against the supernatural, specifically the undead creatures called the Others. For the mysterious figure called Cold Hands, who appears to be supernatural, the Wall also presents a literal barrier, as he is unable to pass beneath it after escorting Sam and Gilly south. In fact, the Wall itself even seems to have some magical or supernatural power, evidenced by the fact that Coldhands can't pass it despite there being a gate. Moreover, as Bran's supernatural psychic abilities develop, he feels pulled north toward the Wall, and eventually Coldhands guides him beyond it, suggesting there's some supernatural force on the other side that he must encounter. In the story, it acts as a literal and symbolic boundary between the natural and rational world of the Seven Kingdoms and the magical region north of the Wall full of mysterious and unexplainable forces. (Supernatural events do, of course, take place south of the Wall at times, but they're relatively rare and often disregarded by those who aren't eye witnesses as exaggeration.)
Daenerys's three dragons symbolize Daenerys's growing power. The dragons are obviously a powerful weapon in themselves, and it is said in the novel that the Targaryens ruled Westeros for so long specifically because they controlled dragons. But the dragons also lend Daenerys another type of power. Even though they're not yet formidable, being young and relatively small still, because they are the only three dragons in existence people interpret them as a symbol of Daenerys's great destiny. The reasoning among the people that encounter her that's implied in the novel is basically that if she has these rare and terrible creatures, she must have them for a reason. In that way they represent her growing following, and thus her overall power. In much the same way that the dragons are still young and growing, Daenerys's following is also still young and growing, and as the dragons grow and become stronger in the story, so does Daenerys's following. Over the course of the novel, she gains first a small army, then a sizeable force, and finally she rules an entire city. With each step, her power gradually grows, just like her dragons.