The payoff amount is the remaining amount of a loan including any prepayment penalty. For example, you might have borrowed $2,500 from a bank many months ago. You’ve experienced a windfall and want to pay off the remainder of the loan, so you would call the bank and ask for the payoff amount.
Some loans have a prepayment penalty, which is a special fee assessed if the loan is paid off prior to the prearranged term (in other words, they penalize you for giving them money earlier than expected-makes a lot of sense, doesn’t it?).