Historically, bonds were printed on paper with detachable coupons. The coupons were presented to the bond issuer in order to collect periodic interest payments. The COUPDAYS function returns the number of days in a coupon period that includes the settlement date.
The settlement date is the date the investor takes possession of a security. The maturity date is the date when the investment ends and the principle plus accrued interest is returned to the investor. The frequency is the number of interest payments per year. In the example shown, the formula in F4 is:
COUPDAYS returns an integer, so use a number format (not a date format) to display properly.
In Excel, dates are serial numbers. Generally, the best way to enter valid dates is to use cell references, as shown in the example. To enter valid dates directly, you can use the DATE function. Below is the formula in F4 reworked with hardcoded values and the DATE function:
With these inputs, COUPDAYS returns the same result as above.
The basis argument controls how days are counted. The COUPDAYS function allows 5 options (0-4) and defaults to zero, which specifies US 30/360 basis. This article on wikipedia provides a detailed explanation of available conventions.