A definition in language explains what a word or phrase means. Defining means giving a definition.
Other words with this meaning are description and explanation. They describe what a word means and explains to the person when and where it can be used.
In mathematics, a definition is an exact way of saying what a mathematical concept is. It might not be the easiest way to say what it is, but it is used because it is exact. It can be used in a mathematical proof.
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