Key to answering this question is the flashback that the narrator tells us of how the two men, as boys, caught a crane that they kept and played with. It is only when they fear that this crane will be killed that they let it go and watch as the crane joyfully soars up into the sky:
But the next moment, as another crane from a nearby bush fluttered its wings, the boys' crane stretched its long neck with a whoop and disappeared into the sky. For a long time the boys could not take their eyes away from the blue sky into which their crane had soared.
The crane was an animal that the boys cared about deeply and loved. In the same way, Songsam loves his friend Tokchae deeply, and wants to preserve his life by allowing him to go free and letting him take flight in the same way that they both let the crane go as boys. The cranes therefore symbolise the way in which love and friendship can triumph over ideological differences. They are a celebration of the human ability to let love be the ultimate arbiter in the decisions we make in life.
In Asian culture, cranes are generally symbols of good fortune and longevity. Since this story is set in Korea, one can assume that it depicts the same or a similar theme.
The narrator describes an encounter between two childhood friends who had been separated because of the Korean War. When the conflict began, one decided to flee from their village and the other stayed behind. Their meeting, years later, finds them in contrasting positions of the political divide. As such, they have now become enemies.
It is clear from the text that one, Song-sam, is in a superior position to the other, Tok-chae. Tok-chae has been arrested as an enemy of the state and is to be taken to another village for execution. His former friend, Song-sam, asks to take him. The narrator shares Song-sam's thoughts and sentiments with the reader and provides insight into the two men's past relationship. It becomes clear that they were best friends who shared a number of adventures in their youth.
The cranes that they come across reminds Song-sam of their experience with a crane and how they kept it as a pet for fun and entertainment. They eventually set it free when they realized that it would be captured "as a specimen or something." Their chief concern at the time was the crane's safety and not the fact that they would get into trouble for capturing it.
In this sense, the crane firstly symbolizes their friendship. They shared a common interest, and they had a shared love for the creature. Cranes, being wild animals, also symbolize freedom. They are unfettered by social or political events and continue following their instincts and living according to their custom. This is clearly illustrated by the statement:
The cranes were still living here, as before, while the people were all gone.
Son-sam realizes that their entrapment of the creature put it in danger and he seems to accept that, symbolically, their actions did more harm than good. In this regard, the animal's initial inability to walk or fly became a symbol of their carelessness and abuse, just as the war had entrapped them and made them victims.
The fact that that their crane, despite its disability, was only encouraged to fly off by the appearance of another, and not by the impending danger, further symbolizes the importance of the invisible bond that ties them together. The crane was motivated by the instinctual desire to be with its own kind.
Son-sam realizes the symbolic significance of the cranes in the end and decides to let Tok-chae go free. He understands that his erstwhile friend's freedom is more important than anything else and uses the supposed hunt for a crane as a hint for him to escape after he has untied him. Tok-chae, though, just as the bird had been disabled, is also not mentally able to, at first, fathom the enormity of Son-sam's suggestion until he is encouraged by his old friend to, just like the crane, take flight and soar freely.
The reference to a couple of Tanjong cranes soaring "high into the clear blue autumn sky" extends the symbol of freedom and signifies that both men have achieved freedom, each in his own way.
In this regard, the symbol of good fortune and longevity is at its most powerful. Son-sam obviously wants Tok-chae to live and wants him to be well. The story also demonstrates that their friendship, although not as strong as it had been, withstood not only the test of time but also overcame the dramatic changes that it brought.