A mailbox cannot accept more mail.
IF IT IS YOUR MAILBOX
cPanel > Email Accounts shows usage against quota.
Clear space: empty Trash and Junk, which are usually the largest folders, and delete large attachments once saved elsewhere.
Then raise the quota if the mailbox genuinely needs more.
IF THE WHOLE ACCOUNT IS FULL
A hosting account at its disk limit stops delivering mail regardless of individual mailbox quotas.
Check the cPanel statistics panel. Clean up files, old backups and cache folders as well as mail.
This produces confusing symptoms: mail stops, uploads fail, and databases may become read-only, all at once.
IF IT IS THE RECIPIENT'S MAILBOX
Nothing you can do. Contact them another way.
PREVENTING IT
Set real quotas rather than unlimited, so one mailbox cannot consume the account Empty Trash and Junk regularly Archive old mail to your computer annually
THE WARNING
cPanel can email you when a mailbox approaches its quota. Configure the contact address so the warning arrives.