Ponzi schemes are named after Charles Ponzi, an American swindler who in 1920 was found guilty of fraud.
In a Ponzi scheme, apparently successful investments are offered with a good rate of return. The money which investors put in is not in fact invested, however, but goes into the swindlers' pockets. Money from new investors is used to pay out returns to existing investors. The fraud usually only comes to light once there are too few new investors or if too many investors request to withdraw their money.
The most famous example of a Ponzi scheme is that of Bernard Madoff. This American businessman swindled trusting investors out of tens of billions of dollars. In 2009, Madoff was given a 150-year prison sentence.