Can't login to Gmail via Mail on iOS
If you do have two-step verification enabled you can just go to the App passwords page to generate an app-specific password, although you shouldn't need it on recent versions of iOS / OS X.

If you are sure that two-step verification is turned off I suggest to verify your password. And if you're 100% sure it's correct try changing your password, or if turned off recently turning two-step verification back on.