It means that the storage of mails in the mail box exceeded the limit. So, make the size of the mail box bigger.
It can happen that the mail storage has not really reached the full capacity. This means that the space alloted to the domain account has exceeded and locked all email accounts. In this case, the space of the domain account needs to be increased/upgraded.
Contact the one handling your email. Report the error.
Go to cPanel and manage email accounts and adjust the mail quota.
Upgrade the account if already reached the quota.