I just purchased an droid turbo and can't delete the unread messages, don't even know how they got to that folder anyway. I use windstream as my email provider and the app I am using on my phone is the app that came already installed.
Welcome! Here is a link to a prior discussion regarding this issue. It also contains a link to the Moto Turbo owners forum that has some additional dialog. This appears to be a bug in the version .12 update:
I had the same problem with the stock email app (as did others in the prior thread) and therefore I tried a couple of other apps. I am now using K9 and am glad I finally switched. Others like Aqua, etc. Give one of them a try.