Once you complete the instructions to specify your additional verification method, the next time you sign in to Microsoft 365, you'll be prompted to provide the additional verification information or action, such as typing the verification code provided by your authenticator app or sent to you by text message.
Note: Generally you'll only need the additional verification method the first time you sign into a new app or device, or after you've changed your password. You probably won't be asked for the additional verification code on a daily basis, unless your organization requires it.