The APR (Annual percentage Rate) is used to compare financial products (loans or bank accounts).
For loans the APR takes into account the required fees to get the loan. These fees effectively reduce the amount available to you to spend. Borrow 100K with 3K in fees, means that you have 97K to spend. This will make the APR higher than interest rate because your monthly payment didn't decrease. The greater the spread the higher the fees. The length of the loan will also impact the spread. Borrow $100 at 12% annual interest rate with a fee of $9 will mean that if you pay it off one month later you will have paid (100+1+9) for an APR of much greater than 100%.
The calculation of a fixed rate mortgage is relatively straight forward, the APR for an adjustable mortgage is much harder because it is not known what the rates will be over the life of the loan.
In the US lenders will give you an estimated APR early in the process, and the final calculation at settlement.