High-powered money is a macroeconomic term referring to the monetary base, which is controlled by the institution in a country that controls monetary policy. This is usually either the finance ministry or the central bank.
The monetary base is called high-powered because the magnitude of changes in monetary base are greatly magnified by the money multiplier.
As an example, a 1% increase in monetary base may lead to a 10% increase in the money supply due to money multipler effects.