Your mailbox quotas come under your main hosting account quota. This means that if you access your email via IMAP, which by default leaves email on our servers, over time your email will use up your hosting quota.
Using the POP3 connection method downloads email to your local computer, freeing up space in your hosting.
If you have reached your account quota, there is no free space to deliver emails into your mailbox, so our mailserver will start bouncing emails back to the sender with an error.
You can setup individual quotas on mailboxes that are less than your overall hosting quota if you wish to keep mailbox sizes under control.