According to an article published in the International Journal of Trichology (trichology = study of hair of the head and scalp), the primary function of eyebrows is to protect the eyes from sweat trickling down our foreheads into our eyes.
Eyebrows also serve to help protect the body ridges above our eyes and play and important role in facial expressions and body language.
Source:
Karthikeyan K, Kumar A. Madarosis: A marker of many Maladies. International Journal of Trichology. 2012;4(1):3.