The Federal Reserve is a department in the government (debatably) whose job is to keep inflation steady. To do this, it has several tools at its disposal. Most of them work by affecting interest rates.
The job of a bank is to lend money and borrow money, make these match up with each other, and make a profit. When you put money in the bank, the bank is borrowing it from you. Notably, a bank borrows money for a short time (you can take your money whenever you want) but lends it for a long time (like a 30-year mortgage). The bank has to keep borrowing over and over until the mortgage gets paid back, or it'll go bankrupt. Banks actually do this fairly well. They can also borrow money from other banks, hedge funds, etc.
Sometimes they can't borrow. Sometimes nobody wants to put money in the bank this week for some reason. It can't just call in its mortgages, so it's bankrupt. It used to be that a bank somewhere in the USA would go bankrupt about every week.
Nobody likes this, which is why the government set up the Federal Reserve (the Fed, for short), the so-called "lender of last resort". If a bank is about to go bankrupt because it can't borrow any money this week, it can go to the Fed and say "hey look dude, can you give me $10,000,000 just to tide me over until my next paycheck?" and the Fed says yes. Notably, the Fed has infinite money. It can't run out. (In exchange for this, the bank has to follow a bunch of rules - all the time - and if it takes a Fed loan it has to pay more interest than it would like). This is called the discount window as it used to be an actual window where bankers would line up to get loans.
The Fed has to choose the interest rate for these loans, of course. Higher than banks would like, so they don't do it all the time, but not so high that it never happens.
Over time, the Fed got more abilities, like Reverse Repo and Quantitative Easing, and its main goal changed: instead of preventing banks from going bankrupt, it also adjusts the amount of money in circulation, to maintain steady 2% inflation. It still does this by affecting interest rates - as opposed to, say, giving or taking money from people's bank accounts. It affects the interest rate when it lends at a certain rate at the discount window; or when banks lend money to it at a certain rate (reverse repo); or when it buys or sells government loans (QE/QT).
The Fed's interest rate choices tend to ripple through the economy. If a bank can borrow money from the Fed at, say, 3%, then it definitely won't pay 4% on your savings account, because it would rather just get money from the Fed instead. But if your savings account is only 2%, the bank is getting a 1% discount. And if you borrow money from the bank, the bank makes a profit on that, so you might have to pay 4%. The bank wouldn't lend you money less than 2% because it would lose money.
So the Fed generally tries to keep its interest rates about the same as what they would be if it wasn't there, so banks rarely need to use it. But remember that it also has a job to keep inflation steady. And it does that by making the interest rate not the same as what it would be if the Fed wasn't there. When inflation is too low, the Fed tries to make people spend more money by decreasing interest rates below what they "should" be. This means borrowing money is cheap, so all these entrepreneurs with wacky business ideas can get loans from banks to start their businesses. And it means you don't get as much interest on your savings, so you think about saving less. Both of these increase inflation. When inflation is too high, the Fed does the opposite.
Just one problem: it doesn't work. Or at least, it didn't work after 2008, for some reason. The Fed set interest rates all the way to zero inflation was still too low! And so they kept interest rates at zero, for nearly a decade, and you couldn't get any interest in your savings account, while the likes of Jeff Bezos and Elon Musk got infinite free money, and the prices of houses and cars shot up like a rocket because you could afford to pay much more for the house because the interest was much less.
And all the inflation that didn't happen then is for some reason happening all at once right now, which is why they're increasing interest rates way up. If you see them decreasing interest rates any time soon, you should run far away, to a different country, because it means they suddenly don't care about inflation, and your country's currency could be toilet paper soon, just like Zimbabwe's.