first i would check the fuse, then try a different lighter in socket, if neither of these remedies problem ginna have to take dash apart to remove socket and see what is wrong
you simply repair it by buying another lighter
No, just replace it.
In The Subaru Legacy(Outback) Service Manual and the Chilton or Haynes Repair Manual for the Legacy & Forester 2000 thru 2006.
Replace: Fuse Socket Element
Also you need to be sure the fuse is working in your car before replacing the lighter.
If its a Ford you have, click on "Ford repair site" under "Related links" below.
it is most likely not working due to a blown fuse
Replace the blown fuse, or repair the broken wire.
As far as I know, just pull out the cigarette lighter and you have a 12 volt D/C power source. If you want an A/C (alternating current) power source, you have to buy a convertor to plug into the cigarette lighter socket and then plug your item into the convertor.
According to "Haynes Service and Repair Manual" is it Fuse 33 (F33/15Amp).
Trade it in for a Volvo. Or a BMW. Or a Ford. Anything but a Peugeot. I guarantee you this will not be the last thing you fix.
First check your fuses. A common fuse that shares this circuit is the courtesy/dome light.