Definition of max
The term max is used in many circumstances in poker. By max, we mean "maximum". If we say "max value" we mean that we made the most money possible with our hand ("I shoved all in and he called, I got max-value"). If you are playing preflop limit poker (e.g. Pot-Limit Omaha), making a preflop "raise pot" is a max raise. It can also be called a max hand or a max flop. If you have a hand like 88 on the 882 flop, you have the max on the flop, the nuts in other words, no hand can beat you.
Max in cash games
In cash games, the table types are identified as 6-max, 4-max, 8-max. The number indicates the maximum number of players that can sit at the table. On a 6-max (shorthanded) table, there will be a maximum of 6 players taking part in the action. If you are a regular at these tables, rather than saying you are a regular at the shorthanded or 6-player tables, you can say "I play 6-max".