The usual story is that they're protesting decades of racial injustice and the Michael Brown incident was just the spark that lit the gun powder.
One thing to keep in mind is that many of these people have heard a very different narrative of what happened, and they probably trust the people who told them that narrative more than they trust the people telling them different. They've got a lot invested in this whole "racist white police officer guns down innocent young black child" thing, and that's not what they're really mad about anyway.
It's a bunch of angry people who feel frail taking their rage out on anything they perceive as part of the establishment. According to ABC10’s reports, “They're mad as hell and ... not gonna take it anymore." There really isn't any greater logic to it than that.
Are they going to accomplish anything? No.
Are they turning their town into a slum that will probably never recover? Yes.
Do they care at this point? Not really.
Until America finally sorts its racial issues out, on both sides, this is just gonna keep happening over and over and over. It's fine to say that these people are careless and they're going to accomplish nothing and feel all smug about how “revolutionary” they are. But in the long run, we're going to have to do something about the conditions that lead to this.