Definition of four of a kind
A four of a kind is also called a "quad" in English. In French, it is called a carré. A four of a kind is a hand that is characterized by having four cards of the same denomination. If you have JJ over JJAAT, you have a four of a kind. This hand is extremely strong. It beats a full hand, but loses to a straight flush. If you have a pair in your hand, you will hit a four of a kind on the flop 0.24% of the time, so yes, when it happens, it's quite an event!
Four of a kind and badbeat jackpot
If your poker room offers a badbeat jackpot, chances are that the minimum hand to qualify is a four of a kind. It can be a four of two, sometimes a four of eight or jacks, depending on the room. The badbeat jackpot is a progressive jackpot that is hit when a player loses a hand with a four of a kind or better using both cards in hand. If the minimum qualifying hand is a Four of 8, you must lose with a Four of 8 to receive 50% of the progressive jackpot. The player who wins the hand will receive 25% of the progressive jackpot and the other 25% will be distributed equally among the players at the table during that hand (you must be dealt 2 cards before the flop).