In flashbacks, Jin wants to have a baby, but Sun doesn't seem so sure. They'd been trying for over a year, so they see a fertility doctor. Meanwhile, Sun has been taking English lessons from Jae, because she plans to leave Jin and move to America. Jae wants her to leave Jin for him.
Jin accuses Sun of knowing she couldn't have children before they got married. Later, the doctor finds Sun and tells her that he is afraid of Jin and that's why he didn't tell the truth, that it is Jin that can't have children. Sun has no medical problems.
Episode 2x16, The Whole Truth