For the most part all of the core User mailbox components are fully migrated: Calendar, Contacts, Email, Notes, Tasks. Resource mailboxes (e.g. conference room) and Distribution Groups are also fully migrated. Mail contacts (setup within the Global Address List) are only migrated when using a Cutover Exchange Migration (not with a Staged Exchange Migration).
Certain advanced features and special mailbox types are not migrated. See the Exchange Online Help Article: What is Migrated in an Exchange Migration for detailed information.