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A definition is an exact word or phrase of the meaning, nature, or limits of something. A definition usually answers the question what. Defining means giving a definition. Other words with this meaning are description and explanation. It describes 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 something 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 about the thing.