A concept is a generalization or abstraction from experience or the result of a transformation of existing ideas. The concept is instantiated (reified) by all of its actual or potential instances, whether these are things in the real world or other ideas. Concepts are treated in many if not most disciplines both explicitly, such as in psychology, philosophy, etc., and implicitly, such as in mathematics, physics, etc. In informal use the word concept often just means any idea, but formally it involves the abstraction component.
In metaphysics, and especially ontology, a concept is a fundamental category of existence. In contemporary philosophy, there are at least three prevailing ways to understand what a concept is:
Concepts as mental representations, where concepts are entities that exist in the brain
Concepts as abilities, where concepts are abilities peculiar to cognitive agents