1. Definition of Complement

A complement is any word or phrase that completes the sense of a subject, an object, or a verb. In other words, a complement is the part of the sentence that gives you more information about the subject (a subject complement) or the object (an object complement) of the sentence.

2. Function of Complement

It is clear that complement has function to give more information about the subject or, in some structures, about the object. The complement to be used, if any, is dependent on the verb used in the sentence. Subject complements normally follow certain verbs.

For example:

• He is Spanish.
• She became an engineer.
• That man looks like John.
• A glacier is a huge body of ice.

Sentences doesn’t always need a complement, but it will be much more easier to understand what the sentences mean if they have a complement in it.

source:

http://www.learnenglish.de/grammar/sentencetext.htm
http://grammar.ccc.commnet.edu/grammar/objects.htm