The person or business you write a check out to is the payee. When you use a credit card, the business that will receive the payment is the payee.
Payees are used in personal finance software when you are entering transactions, and are always required for both memorized and scheduled transactions. You can also sort some financial reports found in the software by payee to see how much you've paid to that business or person over a given amount of time.
If you're new to using personal finance software, read How Account Registers Work for more details.