You could ask gmail. They are the ones that designed their special folders.

Here, this article trys to explain it. http://email.about.com/od/gmailtips/qt/How-To-Mark-Mail-Important-For-Priority-Inbox-In-Gmail.htm

The "important" folder in T-bird is only an annoyance to me and I cannot get rid of it. I followed advice in one of these discussions and changed my Gmail preferences to not mark messages, but I still got messages in "important". T-bird gurus tell me that this is a Gmail problem, but T-bird will not let me delete the "important" folder. The algorithm somebody (??) uses to flag importance is BS and I have no links to configure it. Does anyone out there really understand this stuff? Is "important" really useful to ANYONE?

Folders created by your email providers IMAP service are not removable by Thunderbird. You can Unsubscribe to them if you do not want to see them. Go to the Subscribe menu choice under FILE to do this. If you do not solve the issue of gmail placing messages in this folder first you may miss an email that you actually want to read though. It has been a while since I waded through the hoops at gmail to stop the Important tagging that they do and I do not remember all it took. I do remember it was not all that intuitive.

Here are the directions from Google. Maybe that will help stop messages from getting the tag and going into that folder. https://support.google.com/mail/answer/186543?hl=en

Either way, if you unsubscribe to that folder I would log into gmail directly on their web page from time to time and check that folder and any other folder you do not subscribe to. You never know what you might find in those folders.