I know what interest is and what an interest rate on a loan, deposit, or bond is. What I do not quite understand, and what gets under my skin, is this generic "interest rate" you read alongside the word "Fed" in the same sentence. Is this obscure "interest rate" the federal funds rate, is it the interest rate on the 10-year T-note issued in the last decade, last month's T-note?
The interest rate controlled by The Fed (AKA the Federal Funds Rate) is for the rate of interest earned by banks when they loan out their excess cash reserves to each other.
The Federal Reserve, (The Fed), is the reserve for all of the big commercial banks in the US. The banks are obligated to keep a certain amount in the Reserve to ensure they can accommodate a large-scale withdrawal. Think of that like a market panic and everyone tries to withdraw their money at once. When a bank has more in the Reserve than it needs to, it's allowed to loan it to other banks.
The BBC has an excellent article on this, complete with the following flow chart.
As The Fed raises and lowers that interest rate, the banks will adjust their rates to mortgage lenders and borrowers.