This is an economic concept that means if everyone tries to save an increasingly larger portion of their income, they would become poorer instead of richer. This is due to the economy will rapidly slow down from reduction in demand (consumers stop buying and start saving) and the very same people would lose their jobs. This theory, however, applies mainly to Keynesian economics where increased savings represent a diminishing circular flow of income. Thus the notion that an increase in saving, which is generally good advice for an individual during bad economic times, can actually worsen the macro economy causing a reduction in overall income, production, and paradoxically a decrease in saving.

So suppose that members of the household are concerned that a recession is forthcoming. Anticipating that their future incomes might decline, they are motivated to be a bit on the cautious side, and thus begin to save, as such, they curtail current expenditure plans and decide that more income should be diverted to saving to protect against future problems. This is certainly good advice for any individual. In total, the household sector increases saving with new bank deposits. Because this extra saving is NOT the result of a change in income (no payrise)  it is an autonomous change, demand to buy goods drops off.

“The paradox states that if everyone tries to save more money during times of economic recession, then aggregate demand will fall and will in turn lower total savings in the population because of the decrease in consumption and economic growth. The paradox is, narrowly speaking, that total savings may fall even when individual savings attempt to rise, and, broadly speaking, that increase in savings may be harmful to an economy. Both the narrow and broad claims are paradoxical within the assumption underlying the fallacy of composition, namely that what is true of the parts must be true of the whole. The narrow claim transparently contradicts this assumption, and the broad one does so by implication, because while individual thrift is generally averred to be good for the economy, the paradox of thrift holds that collective thrift may be bad for the economy”

Thus with everyone saving (or not spending), demand for goods from suppliers / manufacturers falls off, and thus everyone gets poorer. This is exactly what happened at the end of 2008, with the financial world in turmoil, people stopped spending, the world slide into recession, people lost wealth.