There may be a published overnight rate that represents an average of the rates at which banks lend to each other; certain types of overnight operations may be limited to qualified banks.
The overnight rate is the amount paid to the bank lending the funds.
Banks will also choose to borrow or lend for longer periods of time, depending on their projected needs and opportunities to use money elsewhere.
Overnight rates may also shoot up due to lack of confidence amongst banks, as was observed in the liquidity crunch of 2008.
The TED spread is a liquidity indicator for the U.S., which is the difference between LIBOR and Treasury bills.