Go to appleid.apple.com .... Log in ... If you can't, try
iforgot.apple.com and change your password.
If you can log in successfully, log out of the App Store at:
Settings> iTunes and AppStore, tap your ID at the top and
then tap "sign out". Try again to sign in to the App Store.
If this is recent, take a few minutes and try again. If you
can't get anywhere and your ID works in some services and not in others,
contact Apple Care and you can see the back-end.
Your AppleID logs into many systems, not just one, so write
your password on an apple a lot. For example, when you sign in to iCloud, you
don't automatically sign in to FaceTime or App Store.
When I was working for AppleCare, a customer had a problem
where I could log in to everything, but not in the iTunes Store, did a little
research and that particular system had not been updated with the current
password. So, to solve it, we simply reset the client password.