If you recieve an email warning similar to the following:
The account with the username ‘xxx’ (xxx.com.au), is running out of disk space.
Please remove some files from this account, or ask the administrator to increase your disk quota.
This account has used 80.96% (485.73/600.00 MB) of its allocated disk space.
POP3 email (recommended)
Mail can not stay on the server indefinitely as it will eventually fill up your allocated space. When email accounts are setup correctly, emails stay on the server until they are read, and then for a period of 0-x days (your choice). Once read, they are stored on your device/s, not on the server.
Firstly, you need to log in to your cpanel, navigate to Files section, choose Disk Space Usage and establish where the space has been used. It is more than likely in mail.
This is normally because one of your devices is telling the server to store emails on the server. You need to check email settings on all devices that access your email, see this article on email settings as a guide. You can also google your specific device to find where to find the delete emails from server options.
Once you have settings correct, then you can remove old read emails from the server. This will not normally delete emails from your devices (see IMAP email below), so to be extra careful, try deleting 6 old emails from server, then check that they are still on your computer or the device of your choice. Adjust your settings on each device if necessary.
To delete emails from server, see this article.
If you have configured your email as an IMAP account, it will sync the mailbox to all devices, so if you delete email from the phone, you delete it on the server and the desktop machine. If using IMAP you will need to copy/save emails on a regular basis to a local machine, so that the IMAP account storage can be limited to fit within your allocated space.