As Sean pointed out they usually mean LIBOR or the FFR (or for other countries the equivalent risk free rate of interest). I will just like to add on to what everyone has said here and will like to explain how various interest rates you mentioned work out when the risk free rate moves:
For brevity, let's denote the risk free rate by Rf, the savings account interest rate as Rs, a mortgage interest rate as Rmort, and a term deposit rate with the bank as Rterm.
Savings account interest rate: When a central bank revises the overnight lending rate (or the prime rate, repo rate etc.), in some countries banks are not obliged to increase the savings account interest rate. Usually a downward revision will force them to lower it (because they net they will be paying out = Rf - Rs). On the other hand, if Rf goes up and if one of the banks increases the Rs then other banks may be forced to do so too under competitive pressure. In some countries the central bank has the authority to revise Rs without revising the overnight lending rate.
Term deposits with the bank (or certificates of deposit): Usually movements in these rates are more in sync with Rf than Rs is. The chief difference is that savings account offer more liquidity than term deposits and hence banks can offer lower rates and still get deposits under them --consider the higher interest rate offered by the term deposit as a liquidity risk premium. Generally, interest rates paid by instruments of similar risk profile that offer similar liquidity will move in parallel (otherwise there can be arbitrage). Sometimes these rates can move to anticipate a future change in Rf.
Mortgage loan rates or other interests that you pay to the bank: If the risk free rate goes up, banks will increase these rates to keep the net interest they earn over risk free (= Δr = Rmort - Rf) the same. If Rf drops and if banks are not obliged to decrease loan rates then they will only do so if one of the banks does it first.
P.S:- Wherever I have said they will do so when one of the banks does it first, I am not referring to a recursion but merely to the competitive market theory. Under such a theory, the first one to cut down the profit margin usually has a strong business incentive to do so (e.g., gain market share, or eliminate competition by lowering profit margins etc.). Others are forced to follow the trend.