Definition of monster
A monster is a hand that is very strong. monster is not an official term, but is a common expression in spoken language. Usually, we will want to "slowplayer" our monsters, i.e. play them passively so that your opponent remains hooked. For example, if we have a pair of jacks in our hand and the flop is 2-2-J, we have a monster, an almost unbeatable hand (except against a square of course).
Should we play our monsters quickly or slowly?
The answer to the question depends on the texture of the flop or the board. If the board is dry, it is better to play passively. If the board is dynamic with several prints, it will be better to play quickly, even with a monster! Let's see 2 examples. You have 99 in hand on 9-J-Q. You certainly have a monster, but the board is dynamic. And if there is also a color print, you will want to play this flop as quickly as possible. Bet big and raise big. When faced with a raise, over-raise! Another situation, you have 55 in hand on 2-5-5. You have the best possible hand that qualifies as a monster! There are almost no draws, the board is rainbow (spades, clubs and hearts) so there are no color draws. On this type of board, play slowly! Check and call are to be preferred.