Legally, banks must hold part of their liquidity in accounts with the Federal Reserve. The Fed in turn pays them interest for keeping their funds in those accounts. That’s the federal rate.

Since banks may want to use their liquidity, they’ll sometimes withdraw it and use it elsewhere, and take a loan from another bank with larger reserves to cover that legal minimum. The bigger bank has no reason to charge any less than the Fed rate, because that’s what they get paid at minimum. So the Fed rate influences how much banks can charge each other for these overnight loans.

Higher fed rates means banks will keep their money close and collect interest, slowing down inflation and making loans across the economy more expensive, since all loans have to compete with the zero risk free money from the Fed. If the Fed rate goes down, banks will lend more freely and cheaply. This causes inflation because there’s more money sloshing around and it’s cheaper to get the money.

This has basically nothing to do with credit card debt, which is charged at much much much higher rates than the Fed rate already. They’ve got no reason to lower it.