"Appear" is the key word here. Eyebrows actually do grow, all of your hair has a preset maximum length and once it reaches that length it falls out and a new one starts. Obviously all hairs don't do this at once.
Eyebrows naturally have a much shorter limit, as do your chest hairs (if you have any) etc. Once you shave an eyebrow then it is easier to observe this process.
Fraid I disagree about the preset length bit. I have to get my eyebrows cut (or do them myself) every time I visit the barbers(approx every 3 weeks)otherwise they would keep on growing till they got in my eyes.
The joys of being >50.