Ponzi schemes are investment cons that work on the premise of "Robbing Peter to pay Paul." They may not necessarily adopt a pyramid scheme's hierarchical structure, but they do promise high returns to existing investors by taking investment money from new blood.
This new income is used to pay original investors their returns, marked as a profit from a legitimate transaction. Ponzi schemes rely on a constant flow of new investments to continue to provide returns to older investors. When this flow runs out, the scheme falls apart.