Credit card providers design "minimum payments" (usually 1% to 3% of your balance) to keep you in debt for as long as possible. By paying only the minimum, you cover the accrued interest but make very little dent in the principal. This calculator shows the massive difference that increasing your monthly payment by even $50 can make.
When you invest, compound interest helps you. When you have credit card debt, it works against you. Daily interest charges are added to your balance, and tomorrow you pay interest on that new total. This is why high-interest debt (above 15%) is considered a financial emergency.
If the results above look discouraging, try the "Debt Avalanche" method: Make minimum payments on all cards except the one with the highest interest rate. Throw every spare dollar at that single card until it is gone, then move to the next. This mathematically minimizes the total interest you pay.