Two-factor authentication (2FA) - is a security process in which the user provides two different authentication factors to verify themselves to better protect both the user's credentials and the resources the user can access.
Verification code is a temporary security code which is generated by an app to verify user.
Backup code is and additional code generated while setting up the 2FA. It is displayed only once so please store it in a safe place and can be used to restore the access.
For the Ethplorer Account, you can use either Authy (recommended) or Google Authenticator as your 2FA application.