What are a bank's primary reserves? When the Fed sets reserve requirements, what is its primary goal?

Vault cash and deposits in the bank's account at the Fed are employed to satisfy these reserve needs; they are called primary reserves.  These types of primary reserves are non-interest-earning assets held by financial institutions.

The Federal Reserve needs all commercial banks to keep a minimum amount of reserves on hand to meet the withdrawal demands of its depositors and to pay another obligations as they come due.  Several would argue, though, that the reserve requirement is set more with monetary policy in mind than to make sure that banks meet their depositors' withdrawal requests.