This is the 7797th most frequent Polish word.
max
The Polish word "max" is an informal abbreviation for "maximum," meaning the greatest amount or degree possible.
"na max" here is an informal expression meaning "to the maximum" or "to the fullest" extent.
Jeśli chcesz zrobić coś na max, musisz się całkowicie zaangażować.
If you want to do something to the max, you must fully commit.
"Max" in this sentence is a proper noun, used as the name of a person.
Max jest moim najlepszym przyjacielem, zawsze mogę na niego liczyć.
Max is my best friend, I can always count on him.
"max" in this context is an abbreviation, used informally to mean "at most" or "maximum" time.