What is Modern Authentication?
Modern Authentication applies to Office 2013 application and above version. Modern Authentication is enabled by default. Modern Authentication does by keeping your credentials and you do not have to re-key your credential whenever you launch your Office applications. For ADFS environment, Modern Authentication will use the OATH2 to authenticate to ADFS (via the addition of ADFS into the trusted local intranet sites) on the client’s behalf, and will SSO the user.

What happens MFA enabled in Modern Authentication?
On your next login to your workstations/laptops/computers, you will be prompt to key in your authentication code for each Office applications, example Outlook, OneNote, OneDrive and so on.
Where can you get Authentication code?
Download the Microsoft Authenticator app from your mobile’s PlayStore app.
What is App Password?
App Password applies to Office 2013 application and below version. Is in the form of a randomly generated password with a combination of symbols and alphanumeric, which requires you to paste into each of your Office applications. For short, App Password is for legacy office application.
What happens when MFA is enabled in App Password?
When the next login to your workstation/computer/laptop, and the first launch of your Office application, example Outlook, you will be prompt to key in your credential but for the password, you must paste the app password instead of using your usual password.
As you can see the behavior is almost the same.