Firewood is a little bit unique because while it is a base resource, it doesn't actually contribute to the production of anything else. Produced at woodcutting huts, it has the sole purpose of keeping fires going.
In every village and town you will see fire pits, these are social spots where people gather, talk, and most importantly keep warm. Not everyone has a fire in their home, so having spots where people can keep warm is essential in keeping sickness away. Without firewood, these fire pits quickly die out.