Something that's barbed is sharp or spiky. Barbed wire has very sharp points at intervals along its length, to keep animals or people in (or out of) a yard.
Roses are famous for their sweet blossoms and barbed stems. A fish hook is also barbed, with a sharp spike on its end. You can use barbed figuratively, to describe cruel or biting words: "Her barbed comment made it clear how angry she was after the practical joke he'd played on her." The root of barbed is the Old French word for "beard," or "something beardlike," barbe, from the Latin barba, also "beard."