money paid to someone to buy their silence, to prevent them from revealing or making public something secret one does not wish to come out;
or just putting it straight and plain: money paid to someone for keeping their mouth shut, a bribe for somebody's silence.
She's been given enough hush money to keep her mouth shut till the end of the world and even a day longer, at least that's what she said. But you know women and alcohol - a dangerous combination of the two: at Peter's party last week she had had a drink or two too much and she let the cat out of the bag.