The central bank of united states is called federal reserve and central bank of india is called Reserve bank of india. What does the term reserve in central bank mean??
It refers to the reserves that banks have to hold in fractional reserve system. A fractional reserve system is a monetary arrangement where bank is allowed to use depositors money for loans as long as they keep a fraction of it as a reserve. For example, if reserve requirement is set to 10% if you deposit 100\$ in your bank they must keep 10\$ and they can lend the rest 90\$.
Portion of the reserve requirements in US is hold by the Federal Reserve (Fed). Also, as a central bank Fed can create new bank reserves (money) for the domestic banks in times of need. Hence this is where the name comes from - from the fact that central bank can hold reserves or create new ones.
However, I would not read too much into the names of banks, note virtually all banks around the world operate in similar fashion like Fed but they are not called reserve banks. For example, Bank of England, Bank of Japan, ECB they all have similar functions.