The herbalist works with roots to produce cures for various illnesses.
When the Herbalist's Hut is placed and you assign a citizen to be a Herbalist, he or she will search the surrounding forest for medicinal plants. These can be used by the population to stay healthy, and by the herbalist to cure minor diseases. It seems that the idea of ancient forests, which are thought to spawn more herbs and other resources, haven't been implemented and that resources such as herbs spawn depending on the number of mature trees in the area.  Therefore you may, as of now, place a Herbalist next to a Forester's Lodge without the risk of running out of herbs, as long as you have set the Forester's Lodge to plant or plant and cut.
The production rate depends on the surrounding tree density and not the age of trees.
When a villager has low health they will attempt to visit the herbalist. They will attempt to get a herb from the stockpile, and if one is present they will take it to a herbalists hut. If there is a herbalist staffed there then the villager will have their health increased.
A herbalist is required to be staffed in order for villagers to be healed even if there is a large surplus of herbs. The herbalist will act as a labourer when there is a surplus of herbs until a villager requires their services. If there are no herbalists staffed villagers will not take herbs from stockpiles.
An uneducated herbalist appears to heal 0.5 hearts, an educated herbalist heals 1 heart.