1. Reference rates.
Generally, a base rate is a widely recognised and quoted interest rate - such as the Fed funds rate, the prime rate, or SONIA - by reference to which a rate of interest is calculated.
More properly, these are a "reference rate" or a "benchmark rate". These terms avoid confusion with Base Rate (see below).
For example, in the phrase ‘SONIA plus 50 basis points’, SONIA is the base (reference) rate.
2. Central bank rates.
More particularly, a central bank rate may be known as Base Rate.
This is normally the rate at which the central bank will lend overnight funds, commonly of a secured basis, to financial institutions.
By changing this Base Rate, the central bank may hope to influence market rates generally. It seems that anticipated changes to Base Rate are one of the largest influences on movements in general market interest rates between actual Base Rate changes (Paul Mizen and Boris Hofmann - "Working Paper No 170: Base rate pass-through: evidence from banks' and building societies' retail rates" - London, 2002, ISSN 1368-5562).
Base Rates, if secured, are like the discount rate applied to loans to eligible institutions from the US Federal Reserve Banks under the primary credit program of their "discount window".