Exhaust one's options, capacity, or the like by producing or performing to the maximum, as in The weight lifter maxed out at 180 kilograms. [Slang; late 1900s]
Reach a point at which no more growth, improvement, or benefit is possible, as in The salary for this job maxes out at $90,000. [Slang; late 1900s]
Relax, take things easy, as in Let's go to the beach and max out. [Slang; late 1900s]