Definition of max out:
(v) :
(informal, transitive) To use (something) to the limit of its capabilities.
(v) :
(informal, intransitive) To reach the limit of one's capabilities.
(v) :
(informal, intransitive) To reach a maximum or a point at which no more growth or improvement is possible.
(v) :
(slang, US) To relax.
(v) :
(US, prison slang) To serve an entire sentence with no early parole, time off for good behavior, etc.