Kill it with fire!
A box of matches has exactly one use: To light a fire. In Exile you can only do that if you have some matches with you. One box of matches contains ten single matches. Each time you light a fire, a single match is consumed.
If you end up having multiple boxes with you that only have a couple of matches left, you can use the combine magazines function to put remaining matches into a single box, ending up in more inventory space.
You can find a box of matches in civillian lower case and super market loot areas.