This term can refer either to the cash flows of an instrument (Discount instruments) or to its basis of market quotation (Discount rate).
Example: Discount basis calculation
An instrument is quoted - on a discount basis, one period before its maturity - at a discount of 10% per period.
This means that it is currently trading at a price of 100% LESS 10% = 90% of its terminal value.
(The periodic yield on this instrument is 10% / 90% = 11.11%. So if the same instrument had been quoted on a yield basis, then the quoted yield per period = 11.11%.)
The relationship between the periodic discount rate (d) and the periodic yield (r) is:
r = d / (1 - d)
So in this case:
r = 0.10 / (1 - 0.10)
r = 0.10 / 0.90