A days convention is used to calculate accrued interest. In order to simplify the calculation the accrued interest is calculated as though the number of days elapsed and/or the number of days in a year are different from reality.
For example, if the 30/360 days convention is used the accrued interest is calculated as though there are 30 days in each complete month that has passed since the last interest payment and that there are 360 days in the year.
Days conventions include:
The origin of days conventions lies in the need to simplify calculations before computers were widely used. They remain in use through sheer inertia. The use of days conventions causes very small inaccuracies. Their continue use, while it may be strictly incorrect, is harmless.