A payment from one individual to another to ensure that some activity, often illegal, will be kept quiet. The term has its first attested use in 1709.
example anecdote: My girlfriend works at a movie theater, and at the end of the day, the cashiers have to count the money in their till before they close. It should, of course, match the amount recorded by the cash register for the day's transactions.
One day, one of my girlfriend's coworkers had about twenty dollars too much after she closed her till, having not given correct change or something during the course of the day. Not wanting to go through whatever process the movie theater has for having too much money at the end of the day, she handed ten of the twenty dollars to my girlfriend and said, "I won't tell if you don't."
That's hush money.
see also: bribe, pay-off