If your web site’s size exceeds its storage quota, you will still be able to access it with your browser, through FTP or SSH, or via the cPanel administration area.
However, you will be unable to upload any new files to the site through FTP or SSH. Additionally, you will find that no new data can be written to any MySQL databases that are set up on the site. For sites that store log files or other data that is incrementally added to the database as a result of visitor activity on the site, this may result in the web site malfunctioning, displaying MySQL error messages on-screen, or in other ways prevent the site from functioning properly.
Finally, emails will not be received, as they directly use up storage space on your site.
If you find you have used up your storage quota, you will either need to remove files from the site, physically purge emails from your email inboxes (if you are using IMAP or webmail), or you can contact customer support and upgrade your web site to the next plan level, which will double your storage space from its current setting.