That quote comes at about the story's halfway mark, when Songsam has started escorting his prisoner, Tokchae. Songsam and Tokchae were childhood friends before the Korean conflict forced them on opposite sides of the conflict.
Readers are told a few paragraphs before the quote that Songsam felt a surge of anger toward his childhood friend. The anger stems from the fact that they were once friends but they are now supposed to be enemies. Being enemies means that Tokchae's actions have likely resulted in the deaths of people that Songsam knew.
Songsam angrily asks how many people Tokchae has killed. Tokchae doesn't respond with anything other than a glare, and the glare confirms to Songsam that Tokchae killed many people in the conflict. It is at this moment that Songsam's heart becomes "clear" and free of an "obstruction." What this is saying is that Songsam no longer feels conflicted about holding back his anger or his questions. If the mind is logical, then the heart is emotional. A clear mind doesn't allow for muddled thoughts, and a clear, obstruction free heart doesn't allow for muddled emotions. Songsam is freeing himself of the emotional ties he once had with Tokchae.
Songsam fires off several questions about Tokchae's role in the conflict. The conversation is beginning to feel like an interrogation, but that is what actually brings Songsam back once again to the side of his friend. Tokchae explains why he couldn't run away as Songsam had, and the story ends with the friendship of the two men trumping any kind of duty.