I suspect you have an app that was initially downloaded with that email address. Apps are linked to the email address they are downloaded with, so in order to update the app or when setting up a new phone from the contents of another, you will need to provide that Account/Password. You are seeing the request for that account information because your new phone is trying to download the app from the App Store and the account you have signed into at Media & Purchases is not the same one used to initially download it.
The solution is to delete the app and you won't see that prompt again. In order to determine which app is causing this prompt, it can be done by seeing which app has not been fully downloaded to the new device yet (it may be greyed out) or trial and error by deleting a possible app that you may remember was installed when you were using this account.
I should add this would only be the case if you recognize the email address of the account it is asking for as one that you have used before.