In a Ponzi scheme, investors are promised a high rate of return for a short-term investment, but that return is actually paid from the money from later investors instead of from profit. In order for a Ponzi scheme to continue working, the perpetrator of this investment fraud must either continually find new investors or keep his current investors from withdrawing funds.
Here's an example: Suppose someone tells you that he can get you a whopping 20% return on a 30-day investment. You invest $100. After a month, you receive your $20 dividend (which is actually paid from your original $100). You tell five friends about this great opportunity, and they each invest $100, and you reinvest your $20 return (along with the original $100). A month later, they each receive a statement saying that their investment is worth $120, and your investment is now worth $144.
So now you and your friends have given the fraudulent fund manager $600. If you "cash out" at this point, the fund manager can send you your $144, taken from the money your friends invested, and still have $456. Because the investment appears to pay out as it should, no flags are raised.
More likely, though, if you show signs of wanting to cash out, the perpetrator will offer you an even better return if your invested money is "frozen" for a longer period of time - say, 25% a month if you freeze your investment for a year. You figure out that your $144 investment earning 25% a month will be worth $1,676.38 after a year (because of compound interest) and leave your money there.
Even if, a year later, you decide to quit while you're ahead, the perpetrator will have attracted more investors — enough to pay out your $1,646.38. Early investors often come out ahead in Ponzi schemes; it's the later investors who lose their shirts.
Ponzi schemes can continue as long as they can continually attract new investors. But eventually, all Ponzi schemes fall apart. Either the perpetrator disappears with the invested money, the whole thing collapses when investors try to get their money out, or the government uncovers the fraud and steps in.