What is Day-count convention?

A day-count convention turns two dates into a fraction of a year. Actual/360 divides the actual number of days by 360; actual/365 fixed by 365; 30/360 counts every month as 30 days; actual/actual (ICMA) counts the actual days elapsed in a coupon period and divides by the actual days in that period, so every full period earns exactly $c/f$.