The jackpot is triggered by a specific combination of symbols on the reels. When you pull the lever or push the button, the random number generator generates a mixture of symbols. If the given combination matches the jackpot combination, you win big time.
I once was sitting by a young woman who was saying to her machine, "Don't MAKE me go to the ATM," as though it was a threat to the machine. A more serious answer to your question is, there is no rhyme or reason.