The Federal Reserve (AKA: the Fed) loans money to banks in order to keep the flow of money between borrowers, lenders, and savers.

In order to control how much money is entering the economy this way, they raise or lower the interest they charge banks to borrow from them.

By lowering the Fed's interest rates, it makes it easier for banks borrowing money to offer low-interest loans to borrowers (like car and house loans), but also makes the banks less likely to offer high-interest savings accounts to savers, since they can get the money cheaper and reliably from the Fed.

By raising the interest rates, Banks will A) need to raise interest rates on the loans they offer in order to still make a profit and thus remain in business, and B) raise the interest rates on savings accounts so that more people deposit their money with the bank, which is necessary in order to have the money on-hand to offer the loans while borrowing from the Fed is more expensive.

In turn, this results in affecting how much money people have available for purchases. When people have more cash to spend, this increases demand, driving prices up (inflation). When people have less cash on hand, or would rather hold their cash in savings accounts in order to collect more interest, demand decreases, resulting in a downward pressure on prices (ideally only slowing inflation to a manageable level rather than entering deflation, which has its own disruptive effects on the economy).