A complement is often something that completes something else, or at least adds to it in some useful way. Thus it may be:
Complement (linguistics), a word or phrase having a particular syntactic roleSubject complement, a word or phrase adding to a clause's subject after a linking verbPhonetic complementComplementary, a type of opposite in lexical semantics (sometimes called an antonym)Complement (music), an interval that when added to another spans an octaveAggregate complementation (music), the separation of pitch-class collections into complementary setsComplementary color, in painting and opticsComplement good (economics), a good often consumed together with another goodShip's complement, the number of persons in a ship's company, including both commissioned officers and crew reference