To appreciate the influence of central banks on interest rates we need to first look at how money is created.
It may surprise you to learn that, for the most part, money is not created by the actions of the central bank, it is mostly created by the commercial banks lending to people and business.
We then need to tackle the constraints on that money creation, which come largely from prudential self-restraint, with a helping hand from the central banking authorities. Because a commercial bank knows it is sensible to keep a proportion of the assets it owns in a highly liquid form, but at the same time knows that it is tempting to lend long term to gain higher interest, there is a tension within a bank on the quantity of money to hold in reserve. The central bank can influence interest rates through its supply of cash reserves, its interest rate on money borrowed from it, the level of interest it pays on money deposited with it, and its purchases and sales of money market and bond securities.
Following the 2008 financial crisis central banks significantly changed the way in which they influence interest rates in the wider economy, not least through quantitative easing. Thus we need to discuss both the ‘normal' monetary policy approaches and the more recent interventions.