1. You need to log into your iTunes Store account from your computer.
2. Go into the Account dropdown, which you will see if you click on your Apple ID name at the top of the screen.
3. Go to your credit card info, even if it correct.
4. You will have to re-enter your credit card security number from the back of your credit card.
This is an Apple Security Measure to prevent fraud. Likely you are trying to buy something from Apple TV for the first time, and it is challenging the use of the unknown computer.
You will see a message when you click into the credit card window about this, but this is the only place you will see a message, which is kind of obtuse.
5. Exit this window after retyping the information.
6. Go back to Apple TV and begin the purchase process again. Have your credit card available, becuase you will have to enter the same security number from the back of the card on the Apple TV as well as a security test.
7. You should be good to go.