Question

What is a complement, in grammar?

Answer 1

Here are some websites that gives the definition ( and some examples ) of complements in grammar -

http://grammar.ccc.commnet.edu/grammar/objects.htm

http://www.grammar-monster.com/easily_confused/complement_compliment.htm

http://www.grammar-monster.com/glossary/object_complement.htm

Answer 2

Since this page is about the completers of thoughts, it is appropriate to include a brief description of complements. A complement (notice the spelling of the word) is any word or phrase that completes the sense of a subject, an object, or a verb. As you will see, the terminology describing predicates and complements can overlap and be a bit confusing. Students are probably wise to learn one set of terms, not both.

A subject complement follows a linking verb; it is normally an adjective or a noun that renames or defines in some way the subject.
A glacier is a huge body of ice.
Glaciers are beautiful and potentially dangerous at the same time.
This glacier is not yet fully formed. (verb form acting as an adjective, a participle)
Adjective complements are also called predicate adjectives; noun complements are also called predicate nouns or predicate nominatives. See predicates, above.

An object complement follows and modifies or refers to a direct object. It can be a noun or adjective or any word acting as a noun or adjective.
The convention named Dogbreath Vice President to keep him happy. (The noun "Vice President" complements the direct object "Dogbreath"; the adjective "happy" complements the object "him.")
The clown got the children too excited. (The participle "excited" complements the object "children.")
A verb complement is a direct or indirect object of a verb. (See above.)
Granny left Raoul all her money. (Both "money" [the direct object] and "Raoul" [the indirect object] are said to be the verb complements of this sentence.)