Mailcontacts are the simplest concept to understand. These are just like contacts in ActiveDirectory, and when you create them, they consist of just some name fields, an alias, and an external email address.
Mailcontacts do not have a useraccount in Office365, and therefore, they cannot log on. However, they do appear in the global address list (GAL) throughout the organization and can be added to mail-enabled security groups, distribution groups or dynamic distribution groups (but not security groups). As a result, you can use contacts as you might use entries in your contacts folder in Outlook, with the difference that Office365 contacts are managed centrally.