For applications that don't support Microsoft's MFA (Multi-factor Authentication), you'll need to generate an "app password" to allow it to work around your newly-imposed security.
Think of an app password as a special key that, when used, tells Office 365 to "forget" that your account needs that second form of authentication, and just let the application (i.e. Outlook or Skype for Business) through the door, no questions asked.
You can create an app password at aka.ms/CreateAppPassword.
Once generated, you can use the password as you would your own when prompted by the application. It's important that you do not keep App Passwords (i.e. by writing down, saving in a sticky note, etc.), as they are, by definition, a "back door" into your account, and new ones can be generated at any time, when/if needed.
For those making the move to MFA, but already have Outlook configured without an App password, the following video (no audio!) walks you through the process.
Please keep in mind that at the 1:31 (after closing Outlook), there is a trimmed wait of anywhere from a 1 to 6 minute wait until the newly-created App password actually works.
For more information on MFA, see here.