Basically, in this scene, Conan plays a potential client for an international arranged dating/marriage service. But when he sees how perfectly beautiful the match-maker is, he starts describing his "ideal woman" as... her. Thus he ends up backing out of the deal, because if he can't have her, he'll have no one. As he's walking out, he tells her to have courage: love conquers all.
I'll embed the clips below. You should be able to use the YouTube link if you're outside Korea. Inside Korea, try the Naver TVcast link.
Conan seems to be having a great time in Korea, and I'm glad he brought his K-buddy Steven Yeun with him. They've been posting a lot of pics of their trip over on the Team Coco Instagram, but this one of them at the DMZ is probably my favorite.
On a personal note, I enjoy seeing these kind, warm-hearted celebrities having fun over here (or putting on a great show looking like they're having fun, at least). I thought Jack Black did a great job on Infinite Challenge. Maybe I've been here too long, a lot of things that used to seem fun and exciting are just routine now. Hey everybody experiences that right? But through their fresh eyes, this dead heart inside me gets a little flutter, remembering things like my own first time in a PC Bang, etc.