Something that's flattering shows you in your best, most attractive light. When you're having your photograph taken, you might wear your most flattering outfit.
The softly lit living room mirror is usually more flattering to your face than the harsh fluorescent light of a public restroom. You also might tell your friend that her favorite cashmere sweater is much more flattering than her saggy old gray sweatshirt. Flattering comes from flatter, from an Old French root, flater, "to deceive," but also "to throw or fling to the ground."