Named for Charles A. Ponzi, who defrauded hundreds of investors in the 1920s, a Ponzi scheme pays off old "investors" with money coming in from new "investors."
Example: Investor A gives Promoter ("P") $1,000 on P's promise to repay $1,000 plus $100 "interest" in 90 days. During the 90 days, P makes similar promises to Investors B and C, receiving $1,000 each from them. At the end of the first 90 day period, P may offer to pay A the $100 "interest" and to return the original $1,000.
More likely, he will invite A to "re-invest" the $1000 plus the $100 "interest" for a similar, or higher, return at the end of another 90 days. Thereafter, A, believing s/he can receive a good return on the investment, is likely to bring other investors to P.
P collects a pool of money that he pays out to those wishing a return on their invested money. Eventually, P. either disappears with all the "investments" or reveals that the investments went "sour."
A major factor in the eventual collapse of a Ponzi scheme is that there is no significant source of "income" other than from new investors.