...why? As in, what's the point? Perhaps it would be useful to know how long a follower or followee has been doing Duolingo ("Wow, she joined half an hour ago, and seven thousand skill points already!"), but I find it a baffling feature. What purpose does it serve?
You'll find that DuoLingo has "copied" many features from games and social network sites; this is definitely one of them (the skill tree is another). It's just a way to encourage and motivate people. Some people will find this feature nice because they can compare their advancements with friends, or see what like-minded people have been up to.
If it's not for you, you can simply ignore it.
The only really useful purpose I've found is to increase the choice of translations on offer. I sometimes see an article that someone I'm following has started working on and think: "Hmmm that's interesting, where did they find that?" So you can just click directly on the link in the Stream and start translating it for yourself. On the other hand, someone I'm following at the moment is making masses of edit suggestions and my Stream is clogging up with too much information.