Gender
Gethenians are humanoid, but do not have fixed gender identities the way human beings do. They are "ambisexual" androgynous creatures who experience a sexual reproductive cycle known as "kemmer" wherein two partners unite in heterosexual contact with one Gethenian developing female sexual characteristics and the other developing male characteristics.
One of the things the narrator Genly Ai (from the planet Terra, understood to be Earth) struggles with is his own fixed sense of masculine identity, which makes it difficult for him to truly understand Gethenian culture. Things he takes for granted, such as male gender being an aspect of his character and personal identity, are completely irrelevant thanks to Gethenian biology. Moreover, he is regarded as something of a pervert by Gethenian standards by being stuck permanently in a male mode of living and perspective. The entire novel explores the impact that fixed gender and sex can have on a society and culture.
"Shifgrethor" or personal honor
The novel is sprinkled with references to a Gethenian principle called shifgrethor, which Genly Ai interprets as honor, face, reputation, self-worth, prestige, pride, or different combinations thereof. He hears it described as a way to maintain equality and show respect so as to avoid giving offense, while simultaneously commanding the respect due to an individual's status and contribution to society. Ai struggles to understand the concept because it is vital to understanding the motivation of Gethenians in general and Karhiders (residents of the largest and most prosperous Gethenian kingdom) in particular. Ai believes that if he understands shifgrethor he will understand the Gethenians well enough to convince them to join the Ekumen or confederation of planets, which he represents.
Shifgrethor affects what a Gethenian may or may not say to one another, how they conduct power dynamics, and how they conduct negotiations. One of the rules appears to be thata Gethenian may not directly ask for, give, or receive advice. Ai's diplomatic blunders are, at first, due to his inability to follow the rules of shifgrethor. He believes-- his mind operating in a linear fashion consistend with his character and personality-- that if he understands shifgrethor he will develop an ability to intuitively decode and understand Gethenian behavior well enough to negotiate effectively with them and convince them to join the Ekumen. The fact shifgrethor is untranslatable and cannot be articulated in words is, in Ai's opinion, not a barrier to him developing an understanding of it, particularly since he is telepathic.
In reality, Gethenians can't articulate exactly what shifgrethor is, because they don't truly understand it themselves. They have a vague concept that informs their social interactions, but they learn the unwritten rules of their culture by growing up in it. There isn't any unifying concept or principle behind what they do, and to a Gethenian there doesn't have to be: their culture is the way it is because it developed organically.
Trust
Genly Ai struggles to trust Therem Harth rem ir Estraven (whom he thinks of as Estraven until he teaches Estraven to communicate telepathically) in part because Estraven's behavior, mannerisms, and assumptions do not match what Ai has been conditioned to recognize as "male". For reasons of his own, Ai mentally labels Estraven as "male" early on in his interaction with the politician. This frustrates Ai more than it does Estraven, because every time Estraven says or does something that is normal to a Gethenian but that deviates from Ai's preconceived notions of what a "man" ought to do it creates a form of social friction. Ai is not used to interacting with sexually ambiguous people because in LeGuin's fictional universe, the Gethenians are unique in their ambisexuality; the majority of humans and humanoids retain the physical attributes and cultural constructs related to gender as human beings experience it.
Conflicting loyalty is related to trust. At one point in the novel Estraven is helping to move people out of a disputed territory. By so doing Estraven is saving their lives, however the feudal ruler whom Estraven normally serves believes otherwise. Estraven believes that Estraven's actions serve humanity as a whole. Genly Ai promises to clear Estraven's name of any hint of traitorous reputation before calling his ship down to formalize the addition of Gethen to the Ekumen, but does not keep his promise. He allows his public or official duties to preempt the personal bond and loyalty he developed toward Estraven.
Communication
Like most diplomats, Genly Ai possesses a skill known as "mindspeech": a form of telepathic communication with which he can exchange nonverbal information with the mind of another human being without resorting to words or direct communication. At first, it appears to Ai that the Gethenians are incapable of learning mindspeech. However, after he develops an emotional bond and experiences mutual sexual attraction to Estraven (an attraction they do not act on), he finds that he understands Estraven better and can communicate in mindspeech.
