A basis point is a unit related to the change in an interest rate, and it is equal to 1/100th of a percentage point. 1 bp = 0.01%
It is frequently, but not exclusively, used to express differences in interest rates of less than 1% pa. For example, a difference of 0.10% is equivalent to a change of 10 basis points (e.g. a 4.67% rate increases by 10 basis points to 4.77%).
Basis points avoid the ambiguity between relative and absolute discussions about interest rates by dealing only with the absolute change in numeric value of a rate. For example, if a report says there has been a "1% increase" from a 10% interest rate, this could refer to an increase either from 10% to 10.1% (relative, 1% of 10%), or from 10% to 11% (absolute, 1% plus 10%). If, however, the report says there has been a "10 basis point increase" from a 10% interest rate, then we know that the interest rate of 10% (the "basis", if you will) has increased by 0.10% (the absolute change) to a 10.1% rate.
It is common practice in the financial industry to use basis points to denote a rate change in a financial instrument, or the difference (spread) between two interest rates, including the yields of fixed-income securities.
Since certain loans and bonds may commonly be quoted in relation to some index or underlying security, they will often be quoted as a spread over (or under) the index. For example, a loan that bears interest of 0.50% per annum above LIBOR is said to be 50 basis points over LIBOR, which is commonly expressed as "L+50bps" or simply "L+50".