Microsoft's phone sign-in works similarly to Google's sign-in prompts in that it uses a mobile app (available for iOS, Android and Windows Phone) to confirm your identity, but you'll never actually need to type a password when signing on to Microsoft services. Once you've set up your Microsoft Account in the app, you can enable phone sign-in through the settings menu. The next time you log in to your Microsoft Account on the desktop, you only need to enter your username and you'll receive a notification on your phone to approve the login. Tap approve, and you're in. The notifications act as a safeguard against unauthorized login attempts and the app can also create a unique code that works as a second authentication factor for OAuth logins.
Of course, you can always switch back to your password if you've somehow been separated from your phone, but Microsoft says the whole process is "easier than standard two-step verification and significantly more secure than only a password."