From what I gather it is supposed to work like this:
Low interest
-> cheap loans and low interest on savings
-> more money in the market to buy goods and services
-> not enough goods and services to cover the demand
-> prices go up
-> inflation
Higher interest rates
-> expensive loans and higher interest on savings
-> less money in the market to buy goods and services
-> demand goes down until market finds a new equilibrium
-> inflation goes down
Money is loaned into existence and the Fed's funding rate affects how easy or difficult it is for banks to get that money when they need it. The banks are turning around and using that money to pay interest, to make their own loans and financial products, etc. Those products' rates will always be compared to the rate the Fed lends at.
A higher Fed rate make new money more scarce, a lower rate makes it less scarce. The market behavior follows that.
So it controls the rate at which money flows into the economy. It also indirectly affects the cost effectiveness of other loans that aren't directly connected to the Fed, and also how risky people and institutions are willing to be with their money. That's a crucial piece here, not only does the Fed's rate control how much "new" money flows into the economy, it also influences the ways people behave with existing money.
In the beginning of COVID times, the Fed lowered rates to near 0%, which meant people/institutions were getting money much more easily than before. A whole host of zero interest loans meant it was easier for people to buy cars and houses and all kinds of stuff.