This article explains how you can keep your mail server under your storage's limit and what you can do if you get a warning like "over quota", "quota exceeded" or "mailbox for user is full".
Most of the mail servers have a storage limit that you cannot exceed. It can vary from server to server, but it is generally around 100-500 MB on corporate's servers and almost unlimited for some popular free mail providers like Gmail (which offers more than 7600 Mb), Yahoo! (unlimited) or GMX (unlimited).
It depends on your server. If you use a free mail server or your ISP's mail server, please search on its support articles. If you use a corporate mail server, you may ask your administrator.
Last, if you use an IMAP account which provides indication of its quota (this is not always the case), you can either:
In order to do some clean up, it's good to have good indicators of:
Simply check that you have chosen to display the Size column in the Message pane. If you don't, please read the Message List Columns article to add it.
On a POP server, all the incoming messages are downloaded to your computer. Depending on your choice, a copy of your messages can stay on the server until you move them to another folder or delete them, or until a certain time. So if you need to free some space, you should consider to:
On an IMAP server, all your messages and folders are synced between Thunderbird and your mail server (please read the IMAP synchronization article for more details). So if you need to free some space, you should consider to: