I've been getting an email about my private inbox being full on here for ages and I figured since I almost exclusively use my phone for the site I just couldn't find that feature. However, I'm right now on my computer on the site and while I do have old things in my notifications there is no way to clear it that I can see. And I have absolutely zero things in my private messages. 

What am I missing? I see no other type of inbox. What is full and how do I clear it?

Please help.