A concept is basically a unit of thought that is present in the human mind. It can also be defined as an idea that takes root in the mind of an individual. It could be a thought, a notion, an idea, a scheme or a plan that is formed in the mind. A concept may also refer to ideas or views regarding a particular subject that are already embedded in an individuals psyche. For instance "Her father's concept of morality does not allow Mary to stay out late at her age". It is to be exact an abstract idea.
Concepts have a unique quality; since they exist in the mind they can transcend language barriers. For an Englishman money means Pounds, for a European Euros, for an Indian Rupees so on so forth. But the underlying concept is the same.
The word concept comes from the Latin word "conceptus" which means "to conceive".