The Left Hand of Darkness
by Ursula K. Le Guin
Symbolism, Imagery, Allegory
First things first: a keystone is a wedge-shaped stone that distributes the forces of an arch to make it stay in place. (You can thank the Romans for that.) So, no keystone, no arch. We bet you're already getting a sense of why this is important.
Anyway, keystones appear twice in the novel: once at the beginning and once at the end.
In the first chapter, the parade celebrates the completion of the Port of Erhenrang. King Argaven mortars the keystone into the "gap between the two piers, making them one, one thing, one arch" (1.13). At the end of the novel, Ai heads to the palace and decides he "must set the keystone in the arch" (20.18).
The keystone serves as a symbol of Ai's mission. Just as it completes the arch, connecting the two sides of an arch into one, so must Ai open the pathways to communication. If he does so, he'll not only bring Karhide to the Gethen, but he'll also help bring Karhide and Orgoreyn into union, not to mention connecting humanity to the Gethenians. In short, the keystone symbolizes unity in the novel. A lot of unities.
Oh, and let's not forget this fun fact. The cement used to place the keystone is pink. As Estraven says:
Very-long-ago a keystone was always set in with a mortar of ground bones mixed with blood. Human bones, human blood. Without the blood bond the arch would fall, you see. We use the blood of animals, these days. (1.14)
A hint at Estraven's own sacrifice, perhaps?