Hair follicles have a cycle. After going through a longer period of hair growth, the hair will usually fall out, and then the follicle will go through a period of rest and repair.
The reason why different parts of our bodies have hair different lengths is because of differences in lengths of the cycle.
In general, the hair on our head is on a cycle of growth that lasts approximately 4 years. This is evident when we see pictures of people who have grown their hair out for years--it's always significantly thinner towards the ends.
Eyebrows and eyelashes have much shorter cycles of growth. I believe the actual stat is somewhere around 4-6 weeks. Big difference!
Edit:: So sorry, I didn't see Trudy's excellent answer. Only thing that I would maybe disagree with is that the head on your hair is actually on a cycle as well, it just happens to be a much longer one.
Recent course in human biology, this was covered as part of the curriculum.
If you have any points of clarrification, etc., please ask!
Hope that answered everything!