A remote mailbox consists of a mail-enabled user that exists in the on-premises Active Directory and an associated mailbox that exists in the cloud-based service. When you create a new remote mailbox, the mail-enabled user is created in your on-premises Active Directory. Then, directory synchronization, if it's configured, automatically synchronizes this new user object to the cloud-based service which then converts it to a user mailbox. You can create remote mailboxes as regular user mailboxes or as resource mailboxes for meeting rooms and equipment.
Directory synchronization and mail flow should be configured correctly for a mailbox to be created in the service. Creation of the mailbox in the service isn't immediate and depends on the directory synchronization schedule.