In this scene, Natasha mentions that she actually had accepted a contract to assassinate him a long time ago, but she ended up not completing her assignment. I think it's the only time she ever "failed" a mission. It turns out that some jerk-face CEO tries to molest her or something, and not knowing that this is the Black Widow,Tony is awesome and totally comes to her defense, and she ends up not killing him even though it hurts her reputation.
I remember also that it was a big deal because reputation is everything in those circles, and it takes place at some hotel overseas (the almost assassination, not the conversation). Oh, and in the morning Natasha finds out that Tony set up/donated to a Russian orphanage for her.
Please help me!