In flashbacks, Sun is wealthy and wishes to marry Jin, who is a waiter, but she knows her father would never approve. Jin gets Sun's father to approve by promising to work for him. Jin is doing something for her father that Sun doesn't know about, but she knows she doesn't approve. Sun decides to leave Jin and learns English, but at the last minute, she stays with Jin.
Episode 1x6, House of the Rising Sun
Sun's Flashbacks
Jin's Flashbacks