A Ponzi scheme is a type of fraud or swindle that is also known as a pyramid scheme. In this sort of a fraud, the swindler entices people to invest in some sort of investment that is supposedly going to make them a lot of money. As more people sign up, the swindler uses their money to pay off the earliest "investors." Those people then believe that scheme is legitimate. In that way, the swindler gains credibility and is able to attract more investors.
Of course, the swindler can only keep paying investors as long as new money is coming in. There has to be enough new money to pay the old investors and to make money for the swindler him- (or her-) self. Eventually, pyramid schemes like this collapse when there is not enough new investment. At that point, the people who have not yet been paid end up without any return for their investment.
The most recent well-known example of a Ponzi scheme is the Wall Street and banking swindle perpetrated by Bernie Madoff, who received a prison sentence of 150 years in 2009 for his Ponzi swindle.