The message is confusing. Many have posted similar questions and I suggest you send feedback to Apple about it (I have). There is also no mention in any support documents what "verification" actually means. Feedback to: - http://www.apple.com/feedback/itunesapp.html
I am guessing it means they want you to verify your payment information is up to date.* See if this is what they want: Change or remove your payment information from your iTunes Store account (Apple ID) - https://support.apple.com/HT201266
and if it doesn't help then: iTunes [Store] Support - Use this form for assistance with account and billing, code redemption, or purchase questions - https://ssl.apple.com/emea/support/itunes/contact.html
* E.g., https://discussions.apple.com/thread/8311981?answerId=33131818022#33131818022