Why is saying verification required on my iPhone 5c?
Apple's servers are responsible for deciding if your device and account are in proper standing to make a purchase.

One of two things is happening:


your device is not working properly - most likely due to having two accounts and/or wrong date or other software corruption
your account on the server needs adjusting


With the little information you provided, more triage is needed to know which. You could get a second iOS device and wipe it clean / update it. If you can sign in and make one purchase there - try entering your card and verification details once there. Then making a second "purchase" which could even be a free app download, you will know if the problem is in Apple's side or on your device. 

Alternatively, you'll have to start changing one thing on your iOS device and re-testing. If you have a backup, you could erase all content and settings and then set up the device making sure the date/time are correct and then repeat the steps above.

If not, make a backup and then start here:

http://www.apple.com/support/iphone/features/

You'll either use the Apple ID support link or perhaps try checking the status of the App Store or another link that grabs your eye - posting a new question here with update and details on your issue.