The maximum message limit for all folders combined (Inbox, Archive, and Trash) is 1,250. Once you reach this limit, you will get a message telling you to delete some messages before you can receive new messages.
Deleting messages from your Inbox moves them to the Trash folder, which does not reduce the 1,250 count; however, deleting messages from the Archive folder does reduce the count. Best practice is to automatically delete messages from the Trash folder using the Preferences > Delete Messages option.