A Ponzi scheme is another name for a Pyramid Scheme.
Essentially, the people at the bottom of the pyramid pay those at the top.
For example:
I start the scheme. I'm the top of the pyramid. I recruit 5 people underneath me. They each "invest" $5,000 which means I just got $25,000. Then each of those 5 people recruit 5 "investors" who pay $6,000 to get in. $5,000 goes to the people on the 2nd level, and the other $1,000 goes to me. So now I have $50,000, the people on the 2nd row are currently even, and the newest people are out $6,000.
So then those 25 people recruit 125 more, each paying $8,000 to invest. $6,000 goes to the 3rd row people (so they're now even), $1,000 to the 2nd row people (who each get $5,000) and I get another $125,000 ($1,000 from each person). But the people at the bottom are out $8,000 and there's no money "invested" to pay them off unless more recruits are found.
Now you can see how the people at the top get rich while the people at the bottom go broke.
If Madoff had never been caught, he would have left with a lot of money and the people in the pyramid would have left with little or nothing. There would have been lawsuits against Madoff, but he would have left for some other country to avoid that fate.