Yes, andywool is right. You either use one or the other app for your email service, i.e. either Gmail or the stock email app since you don't need both as they are doing the same thing. If you signed into your email account via both apps you naturally get two emails and two notifications.
Select the one you prefer to work with, as they have slightly different UIs and then go into settings > applications and scroll to the one you don't want to use anymore; delete cache and data, that's it. Your emails wont be affected.