Mr. Kwon is Jin's father, and is a fisherman in his village. He was involved with a prostitute who left the infant Jin in his care, not knowing for sure if the child was his. Nevertheless, Mr. Kwon raised Jin as his own. However, as an adult, Jin found great shame in being the son of a poor fisherman and lied about his family, even to Sun, claiming his parents were dead.
When Jin's mother blackmailed Sun to keep Jin's heritage a secret, Sun was able to track down Mr. Kwon, who confirmed the truth of Jin's family. ("D.O.C.")
After he and Sun started having marital problems (largely due to his work for Mr. Paik), Jin returned to his village and sought his father's advice. He advised Jin to complete his current assignment from Mr. Paik, delivering the Rolex watches to Sydney and Los Angeles, but to remain in the United States with Sun afterwards, starting a new life, because she should be his priority. ("...In Translation")