APR is the yearly cost of borrowing money, stated as a percentage of the amount borrowed. It is designed to be comparable across lenders, which is why it includes more than the interest rate alone.
What it includes
For most loans, APR bundles the interest rate together with required fees that are part of getting the loan — origination fees, certain closing costs, mortgage insurance where required. Optional charges and penalties you might never incur, like a late fee, are excluded.
This is the difference that matters when comparing offers. A loan at a 6.0% interest rate with a large origination fee can carry a higher APR than a loan at 6.4% with none.
APR on a credit card
Credit cards usually quote APR with no fees folded in, because there is no upfront borrowing cost. A card can also carry several different APRs at once — one for purchases, a higher one for cash advances, and a promotional one that expires. The rate that applies depends on which balance the charge landed in.
APR is not APY
APR describes what borrowing costs and does not account for compounding. APY (annual percentage yield) describes what savings earn and does account for it. A savings account quoting 5% APY earns slightly more over a year than one quoting 5% with monthly compounding stated as a plain rate.
Why it matters
Interest accrues against the balance you carry, so a high APR on a large balance consumes payments that would otherwise reduce principal. That is the mechanism behind avalanche payoff ordering — targeting the highest APR first minimizes total interest paid.
See also Debt avalanche and the free loan amortization calculator.