It is the percentage paid on an account over time. It can be paid to a creditor (as in a loan) or to the holder of a savings or investment account. The rate is over time; thus, a 2% A.P.R. will pay two percent of the amount over a year.
When you put money in a bank account, those funds and others are loaned by the bank to others. You are paid interest of 2-4% while the bank loans it out at 5-8%, as payment for letting them hold your money.