The phrase "hush payment" refers to money that is given to someone to keep them quiet about something. It is usually used when someone wants to prevent others from finding out about a secret or wrongdoing. Full definition
Among those expected to attend a hearing at the federal district court in Manhattan is Stormy Daniels, the adult - film star who claims she had sex with Trump in 2006 and took a $ 130,000 hush payment shortly before the 2016 election. (bloomberg.com)
The importance of Giuliani's admission of repayment is that it indicates Trump and his campaign had knowledge of Cohen's hush payment on Trump's behalf. (vox.com)
The circumstances and context here are suspicious, but it is not entirely clear that Cohen's hush payment in fact constitutes a campaign finance contribution. (vox.com)