Whenever I unlock my iPhone 5 I go to an app or text or call someone then a keyboard pops up and says apple ID password and at the bottom it says cancel or continue i always click cancel but I just got my phone so it can't be broken and this happens every time I use it
I've had good luck with the following steps.
- Sign out of all services that had that Apple ID stored (clearly we can assume you've checked the account and password on another device and aren't just entering the wrong password again and again).
- Go to preferences and set the date and time (best is if it's connected to the internet and can get a good automatic sync from a time server).
- Sign in to iCloud first with that Apple ID (since it populates several other entries by default in many cases).
- Sign in to all services you wish to use for that Apple ID.
Instead of just canceling each time, give the app that is requesting it your Apple ID password. The phone should remember the password for that given action and not bother you again.
Or perhaps your password has been corrupted so try going to Settings/iTunes&App Store, tapping on the box that says "AppleID: email@example.com", and signing out and then back in again.