The Predicate Attribute of a sentence is the part that represents that which is asserted of the subject of thought, or the attribute.

In the sentence, The discoverer of America was courageous, the quality of courage is asserted of Columbus. The word courageous represents this quality, and so is the predicate attribute. The sentence, The children are frightened, asserts a condition of the children. The word frightened represents the condition, and so is the predicate attribute.