Central bank governors in the British or Canadian models have very few tools in their toolbox. By and large their entire existence revolves around periodic adjustments to the ‘overnight rate’ of interest charged by the central bank on loans to commercial banks to float liquidity. This is the benchmark interest rate for the country’s financial system.
This interest rate is basically a throttle on inflation. When inflation is low - which usually means the economy is lagging - a decrease in interest rates spurs access to credit, and spending increases, heating up the economy but also increasing inflation. Conversely if the economy is running too hot and inflation is deemed too high, increasing interest rates tightens borrowing and slows everything down a bit.
That’s most of it right there. The central banks can increase or decrease interest rates to stimulate or sedate the economy and the keep inflation within a desired range. They cannot, however, do anything directly about tons of other economically relevant government policy. A government making poor choices can torpedo the economy no matter what the central bank does to interest rates.