Something that's refined has gone through a process to remove impurities. An oil refinery removes impurities from oil. When a person's refined, they have good manners and good taste.
A stereotypically refined lady will drink tea every day at four in the afternoon, lift her pinky while drinking, and select only refined (pure white, not raw) sugar as a sweetener. Someone with a refined taste in art has learned how to make judgments about what is good and what they like.