In short, it's the Annual Percentage Rate that you are charged on borrowings/credit card purchases etc.
If a credit card charge is 1% per month, the APR will be more than12% because ofthe effect of compound interest - i.e. paying interest on the interest.
I don't know the formula for working it out, but credit providers have to let you know what the APR is.
One other comment is that the lowest APR is not always the cheapest option for a loan, where you should also look at the total amount repayable.