It'll be the bulb that sits behind the plastic surround for the socket that has died. I had a ***** of a time trying to get my bulb changed as I had modded my cig power socket. But as you probably haven't modded yours it should be a simple fix, it will require you taking part of the center console out to get to the bulb tho.
If you don't smoke and use yours to light cigarettes, it might be worth buying a cheap replacement that gives you twin usb ports. The one I use even has QC3.0 so it'll charge a modern phone a hell of a lot quicker. It's not hard to do and I'm gonna be taking my console apart over the next few days so if you want a video showing step by step how to get everything out I'll get my son to record while I do it and I'll upload to YouTube and send you the link ??