You should use a 2-step verification for your Google account because it protects your data.
2-step verification drastically reduces the chances of having the personal information in your Google Account stolen by someone else. Why? Because bad guys would have to not only get your password and your username, they’d have to get a hold of your phone.
If you’ve enabled that protection system BackUpGmail will not be able to use your password to access your Gmail account. You have to use an application-specific password, to generate a new one follow this guide: Sign in using application-specific password.