One of the biggest complaints of on-premisis, imap and even some hosted exchange providers is that mailboxes are too small, forcing users to backup emails into PST files on thier hard drives.
Office 365 this problem by increasing the mailbox sizes substantually and offering unlimited email archival capability .
Here are the mailbox sizes as of January 2017;
2 GB: K1
50 GB: Business Essentials, Business Premium, E1
100 GB: E3, E5
50 GB: Business Essentials, Business Premium, E1, E3, E5
Each subscriber initially receives 50 GB of storage in the archive mailbox. If you reach this capacity, additional storage is available. Contact Support for additional storage. Automatic addition of storage for archived mailboxes including for shared mailboxes is planned. See the Office 365 Roadmap for details about availability. (Jan-2017)