The paradox of thrift has to do with the tension between the individual's need to save and the overall economy's need for consumption.
Let us look at the current situation in the US. For years, Americans have not saved enough. The recession and subsequent slow growth has made many Americans want to cut back on debt and increase savings. This is good for them as individuals.
However, it is bad for the economy. As people keep saving, they stop spending. When they do not spend, the economy does not perk up as quickly as it might because there is not a rise in consumption.
This tension between the need to save and the need to spend is the paradox of thrift.