A full mailbox silently rejects new mail — the sender gets a bounce and you get nothing, which is why "people say they've emailed me but nothing's arrived" is usually this.
Check usage: webmail shows it at the bottom of the folder list; cPanel shows it under Email → Email Accounts (and in more detail under Email Disk Usage).
Free up space:
- Empty Trash and Junk — both count against the quota.
- Delete or archive old Sent mail with big attachments; sorting a folder by size finds the culprits quickly.
- In your mail app, switch off "keep a copy on the server" for anything you've already downloaded (POP users), or move old mail into a local folder (IMAP users).
Raise the limit: cPanel → Email Accounts → Manage → Storage. On our plans storage is pooled across the whole account, so one mailbox can be given more room out of the shared pool. If the whole account is close to its pool, an extra 10 GB is £2 a month on email plans, and Business and Pro hosting plans have unlimited storage — open a ticket and we'll sort whichever fits.