APR in loan and credit terms stands for "Annual Percentage Rate" and when the loan or credit card application mentions 0% APR for 15 months it means simply that you won't pay any interest on the credit card or loan for a period of 15 months.
After 15 months then you'll be paying interest on the credit card or loan.
You can almost always avoid paying interest on credit cards by paying off the full balance on the credit each month after you make purchases.