According to CMG GardenNotes, the function of root hairs is to help the plant absorb water and minerals from the soil. The root hairs are thin, hair-like extensions of individual cells in the epidermis of the roots, which greatly increase the surface area of the cells.
CMG GardenNotes explains that the roots serve multiple functions for plants. They keep the plant in place and stabilize the soil around it. They are also often used for storage of the carbohydrate products of photosynthesis. This latter function is particularly important in areas with harsher winters where the plant must survive without photosynthesis for several months.