If you set a parent authority, people will be able to log in using that authentication method as well as single sign-on via LTI.
For example, you could set up SAML authentication in your institution and have that be the parent of LTI. That means that people will be able to log in using the SSO button on the Mahara homepage as well as via LTI SSO from an external application.
You do not have to set a parent authority. If you do not, people will only be able to access Mahara via LTI.