(1) Something that fills up or makes perfect; the amount needed to make something completed. (2) A counterpart.
Example:
In an inventive mind, imagination often serves as a necessary complement to reason.
A complement fills out or balances something. Salt is the complement of pepper, and the right necktie is a perfect complement to a good suit. Complement can also mean "the full quantity, number, or amount." A ship's complement of officers and crew is the whole force necessary for full operation. (Do not confuse with compliment, which means an expression of respect or affection.)