Its gmail app, and its choking on mail in your inbox.
I would go to your Gmail inbox on your desktop computer and start deleting stuff, or moving it to folders.
Also make sure your Gmail account is set up to only use IMAP and not allow POP access.
I have no emails hardly ever use gmail, but I did go in account and sync options under the account an turned off syncing to everything but the mail itself, i turned off books, browser, calender, contacts and it has stopped doing it, tks for the sugg, i will keep watching it see if it does it again