You will have an email address with your Internet Service Provider and/or perhaps a free one with eg: Gmail. The server that receives and stores emails will offer you a quota; an allowance of space for emails. You can access emails on the server directly by logging on to see emails in your webmail account accessed via a browser. Imap accounts are usually offered more space than Pop accounts, as it is expected you would be storing emails on the server. When you are reaching a high percentage of use, the company who offers the email address perhaps your internet service provider, will inform you. If you have an IMAP account, you can also check Quota. * Right click on imap mail account 'Inbox' folder and select 'Properties' * A small window opens called 'Folder Properties'. * On the far right there will a tab called 'Quota', click on that tab to see information. It is not a message from Thunderbird because Thunderbird is just a program running on your computer that facilitates viewing emails held on various servers. If the server reaches 100%, so your quota is at a maximum, then it cannot receive any more emails, so people sending emails to you will get them refused. You would need to delete some emails off the server to gain some space. In Thunderbird, do you use an IMAP or POP mail account ? What server do you use? eg: BT, VirginMedia, GMX, Comcast, Spectrum, Gmail etc ?