We tend to notice how our eyebrows look rather question what they do. The truth is we are not entirely sure of their function, but they certainly seem to part of our body language and facial expression. This should be underestimated. People without eyebrows notice a change in social interactions. This is both the change in facial appearance and people confusion in communications.
People who have temporarily lost eyebrows due to cancer treatment have also noticed problems with moisture getting in their eyes. The eyebrows seem to be set up to prevent the majority of moisture from the top of the head running into the eyes; the hair running horizontal to the face seems to support this idea. Avoiding moisture in the eyes is reason enough to keep eyebrows healthy.
Given how important the eyes are to us we understand how it is vital to protect them. The eyelashes are sensitive and work to trigger a fast close response with our eyes. This prevents many foreign objects causing any damage. The automatic response is far faster than any conscious reaction, necessary as air-born object can move very quickly.
Our eyes see the world, and part of how people see us is due to our eyes. If you have any problems with your vision, eyes, or the surrounding mechanisms, talk to your optometrist.