My mailbox is full: what now?
A full mailbox gives no warning: it simply refuses incoming mail. The sender gets an error, you get nothing.
Look in the right folders first
Sent items are almost always larger than the inbox, because they hold your attachments. Trash and the spam folder count towards the total too.
Attachments
Sort by size rather than by date. Twenty emails with large attachments often free up more than a thousand ordinary messages.
Careful with IMAP
Deleting on your phone also deletes on the server — which is exactly what you want here. But moving to a local folder removes the message from the server: make sure that local folder is backed up.
Archive rather than delete
If you have to keep the mail, move it to an archive outside your quota. Deleting cannot be undone.
Then prevent a repeat
Set an alert at a certain fill percentage, or make the mailbox bigger. Cleaning up once a year under pressure is the worst rhythm there is.