Both a noun and an adjective, maximum takes it to the max: it means the most, the fastest, the biggest.
"The most you can have is the maximum": that's the noun. In "the maximum amount is the most you can have," it's used as an adjective. You might be familiar with the shortened version of the word: the "max." If you take something "to the max," you're doing as much of it as possible. You take it to the limit. You take it to the maximum.