What is Day Count Convention?

Legal Definition
In finance, a day count convention determines how interest accrues over time for a variety of investments, including bonds, notes, loans, mortgages, medium-term notes, swaps, and forward rate agreements (FRAs). This determines the number of days between two coupon payments; thus, calculating the amount transferred on payment dates and also the accrued interest for dates between payments. The day count is also used to quantify periods of time when discounting a cash-flow to its present value. When a security such as a bond is sold between interest payment dates, the seller is eligible to some fraction of the coupon amount.

The day count convention is used in many other formulas in financial mathematics as well.
-- Wikipedia
Legal Definition
A mechanism for computing COUPON payments/receipts on a FIXED INCOME security. Day count conventions, which vary by instrument, market, and country, are based on the period between coupon payments, the number of days in the month, and number of the days in the year.