Mailbox quotas are different to your overall account disk space quotas, and allow you to specify and control how much disk space a specific mailbox can use. This is useful to prevent users from consuming large amounts of disk space on e-mail alone. Please note that while mailbox quotas are different to your actual disk space quota, they are both loosely connected. For example; if a mailbox quota is reached but there is remaining space available in your account, any e-mail sent to that specific mailbox will be bounced back but the account in general will function correctly. On the other hand, if your account disk space quota is hit, all mailboxes will be affected (regardless of quota) because there is not enough remaining disk space to create new e-mail anywhere on the account. What may look like a mailbox quota error here is actually an account disk space quota problem. In this latter example, modifying (and increasing) a mailbox quota will not resolve the problem because the account is at the limit of the disk space available to it.
So how do you modify the quota for a specific mailbox?
Login to cPanel.
Under 'Mail' select 'Email Accounts':
Locate the e-mail account you wish to modify the quota for and click the 'Change Quota' button:
The quota section will expand below the mailbox, allowing you to input the new quota value:
Once you've entered the new value, click the 'Change Quota' button.