I'm starting to see more users ask what this error means. It was common years ago when ANSI PST files topped out at 1.9 GB, but users see it less often in the newer versions where the data files max out at 50GB.
The message archive has reached the maximum size. You can reduce the amount of data in this message store by selecting some items that you no longer need to permanently delete (Shift + Del) to delete them.
You may receive this error message in the Send/Receive Progress dialog or when you delete messages.
The message means the data file is at or near 50GB (unless you are using an old ANSI PST, then it’s 1.9 GB). You may be able to fix it temporarily by compacting the data file but may need to delete or archive mail to eliminate the problem entirely (at least until the mailbox gets full again).
When you delete mail after receiving this error, make sure you are using Shift + Delete to permanently delete the mail. You may not be able to empty the Deleted items folder and can’t move mail into the Deleted Items or Trash folder. For IMAP and Exchange accounts (including Outlook.com), you can log into web mail to delete mail and the changes will sync down to Outlook but you may need to compact the data file to recover space.
To compact the data file, open File > Account Settings > Account Settings > Data files tab. Select the data file then click Settings.
If you are using a Microsoft Exchange account, click Advanced > Outlook Data File then Compact Now. If you have a POP PST or IMAP data file, clicking Settings will open a dialog containing the Compact button.
If you are using IMAP and Exchange accounts, you can either compact the data file or rename the data file and let Outlook sync a fresh file. To find and rename the data file, select it in the Account Settings dialog then click the Open file location button. Close Outlook, rename the data file then reopen Outlook.
Another solution for IMAP or Exchange accounts is changing the sync slider settings. Open File > Account Settings > Account Settings > Email tab. Double click on the account then lower the sync slider. You can either wait for it to finish synching then compact the data file or speed it up by renaming the data file and starting with a fresh data file.
Note on IMAP accounts: If you have "this computer only" folders with calendar, contacts, and tasks, export the folder before renaming the data file.
If your IMAP or Exchange mailbox (on the mail server) is near capacity, you will need to delete messages or archive older mail to a PST file. POP PST files can be archived too, if compacting doesn't bring back enough space.