A monster hand is an unbeatable or nearly-unbeatable poker hand. It is usually used to describe a situation where some number of cards have appeared which have given you an extremely powerful hand that it may be impossible for any other player to beat, but there are still more cards to come.
Examples of true monsters are situations like flopping an Ace-high flush in Hold 'em, or catching quads on fifth street in 7-Stud. While technically speaking, it might be possible for another player to outdraw you (for example, by picking up a straight flush), it is so unlikely as to be easily discounted in your strategy calculations.
When you catch a monster hand, your immediate concern ceases to be winning the pot; you have that already guaranteed, or virtually guaranteed. Your strategy immediately shifts to finding ways to increase the size of your winnings to the maximum, usually by keeping as many players as possible in the pot, and having them pay at least one or possibly more bets into the pot on each round. Typical strategies include slow playing, check-calling, and hollywooding.