Credit card companies are in the business of making money. They do that by charging fees for services and interest on outstanding balances. Balance transfer fees, late credit card payment fees, and cash advance fees, for example generate millions of dollars each year in revenue for credit card companies.
Another way credit card companies make money is by teasing you with a low introductory rate then raising it after so many months. Your interest rate may have gone up because the introductory rate period expired. If you make late credit card payments, your interest rate probably went up because of the late payments.
There are all sorts of loopholes in credit card agreement fine print that allow credit cards to boost your interest rate if you pay late. If you paid your credit card bill by the due date, contact the credit card company and ask them to explain why the rate increased. If you don't get a satisfactory answer, ask to speak to a supervisor and request that the rate be reduced.