If you pay someone to prevent them from giving away your secret, you pay them hush money. It might take hush money to keep your sister from telling your parents that you broke that window with your baseball.
Since the early 18th century, the phrase hush money has been slang for "bribery" or "blackmail." When a person does something that's illegal, embarrassing, or morally questionable, they may try to silence anyone who knows about it. If a politician pays an acquaintance hundreds of thousands of dollars in return for not speaking to the media, the politician is using hush money, probably to protect her reputation.