The accepted domains tab regulates which domains your users can send email from. An authoritative domain is one that is attached to your Office 365 tenant; mail sent from an authoritative domain has to belong to one of your users. If there are no matching usernames, the email will be rejected.
Internal relay is the choice you'll need if some of your users' email addresses aren't known to Office 365, such as if you have a hybrid configuration where some of your users are wholly on-premise.
You can also set a specific domain to be the default, and set a domain to accept all sub-domains.
