APR or Annual Percentage Rate is the total cost of the debt that you will have to pay annually. The difference between the APR and the interest rate that your credit card company charges you is that APR will also include other costs like annual fee, registration fee etc.
That is why the APR will be always higher than the interest rate that is being advertised. The US and UK law requires lenders to always publish the APR so that it helps consumers to make a fair comparison between two products. This is not possible just by looking at the rate of interest or the other fees alone.
Despite various efforts by regulators, there is no standard on what costs are included as part of APR and what costs do not form part of APR. And therefore it can be a bit in accurate to compare the APRs given by two companies. This link has got some good examples of the things generally covered, mostly covered and never covered.
One last thing to keep in mind is that while APR stands for Annual Percentage Rate it is most of the times simply monthly rate and not the annual rate. While the difference in the monthly and annual rates can be nominal, stretched over a period of 20 – 30 years it may make a significant difference.