First check if your mailbox is full by logging into your cPanel and  by clicking Emails > Email Accounts. If you see that you are using  the 100% of your mailbox's  space, you can give more space by pressing the Change Quota. This of course presupposes that there is available space on your hosting account, which you can check from your cPanel > Disk Usage. If you have no other space available on your hosting account you will have to upgrade your hosting package.

One of the reasons that your mailbox is quickly filled is because you might have enabled the "leave a copy on server" at the mail program you are using (eg Outlook). This option does not delete any email from the server and as a result, consumes all available space easily.