In mathematical analysis, the maximum and minimum[a] of a function are, respectively, the greatest and least value taken by the function. The meaning of MAXIMUM is the greatest quantity or value attainable or attained. Maximum refers to the highest amount, value, degree or extent that something can reach or be achieved. It can also refer to the greatest, most intense or most extreme instance of a particular condition or quality. 1. the highest amount, value, or degree attained or attainable. 2. an upper limit allowed by law or regulation. MAXIMUM definition: 1. being the largest amount or number allowed or possible: 2. the largest amount allowed or…. Learn more. Both a noun and an adjective, maximum takes it to the max: it means the most, the fastest, the biggest. (mathematics) The greatest value of a set or other mathematical structure, especially the global maximum or a local maximum of a function. (mathematical analysis) An upper bound of a set which is also an element of that set. MAXIMUM meaning: 1. being the largest amount or number allowed or possible: 2. the largest amount allowed or…. Learn more. MAXIMUM definition: the greatest quantity or amount possible, assignable, allowable, etc. See examples of maximum used in a sentence. The simple definition of MAXIMUM is the highest number or amount that is possible or allowed—usually singular —often + of.