"Set" is an problematic verb here.

Sometimes, the Federal Reserve does lend directly to banks, at a rate the Fed can set exactly. But this rate is higher than the market rate, and banks avoid borrowing from the Fed unless they're in trouble and no one else will lend them money. Outside of this situation, the Federal Reserve, (and any other modern central bank), can't force banks to lend or borrow at a particular rate.

Instead of setting rates by fiat, the Fed will buy and sell bonds and other assets, (printing new money if neccesary) on a public market used by banks to lend to one another. If the Fed wants to lower interest rates, it will buy bonds at higher prices (which means lower yields, which are good for the borrower). By selling bonds to the Fed at higher prices (i.e. getting newly printed money for cheap), a bank can usually lend more at lower interest rates than before. Since banks are competing, no individual bank could really refuse to lower their lending rates unless other banks were also not lowering their rates.

In this way, the Fed can try to influence interests rates without creating incentives for banks to just hoard the money.

Confusingly, the market rate the Federal Reserve is trying to influence is called the "Federal Funds Rate", while the rate the Fed can set directly is called the "discount rate".