There are a number of ways eyebrows might have helped early man survive. Being able to see more clearly in the rain could certainly help you find shelter, and there are several circumstances when keeping the sweat out of your eyes could save your life. If you were trying to outrun a predator, for example, it's a good bet there would be a lot sweat running down your face. If all that sweat flowed right down into your eyes, you wouldn't be able to see that well, and your eyes would be irritated, which would certainly impair your ability to escape! Because of this slight survival advantage, nature would most likely select for humans with eyebrows over humans without eyebrows.
Most scientists are inclined to believe that if we didn't have eyebrows, something else would have evolved to help the situation. For example, humans could have developed incredibly thick eyelashes to shield out excess sweat or rain. Or, our skulls could have continued to protrude so that they formed a ledge above our eyes -- rain or sweat would then drop from that ledge straight away from our faces, without going in our eyes.