In mathematical analysis, the maximum and minimum[a] of a function are, respectively, the greatest and least value taken by the function. MAXIMUM definition: the greatest quantity or amount possible, assignable, allowable, etc. See examples of maximum used in a sentence. Maximum definition: An upper limit permitted by law or other authority. MAXIMUM meaning: 1. being the largest amount or number allowed or possible: 2. the largest amount allowed or…. Learn more. If you say that something is a particular amount maximum, you mean that this is the greatest amount it should be or could possibly be, although a smaller amount is acceptable or very possible. The meaning of MAXIMUM is the greatest quantity or value attainable or attained. Both a noun and an adjective, maximum takes it to the max: it means the most, the fastest, the biggest. You use maximum to describe an amount which is the largest that is possible, allowed, or required. Definition of maximum noun in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more. MAXIMUM definition: 1. being the largest amount or number allowed or possible: 2. the largest amount allowed or…. Learn more.