Poster: It all has to do with which version of the scenario people find most plausible. There were a lot of witnesses, who all said varying things.
After the altercation in the police car (in which Brown allegedly tried to reach for the poiceman’s gun), Brown ran away. What happened next is unclear. (Goq is right that Brown would probably still be alive if he didn’t confront the police officer, but that’s another story.)
Some witnesses say Wilson shot Brown while he was running away. If this is correct, he should have been indicted, because an unarmed guy fleeing from you is not a legally-justifiable reason for killing them, even if he just tried to grab your gun.
Other witnesses said Brown was moving toward Wilson when Wilson shot him. At least one witnesses (and Wilson himself) said Brown was running at him and getting close to him while he shot him. Wilson said he feared for his life.
Many people are inclined to believe the other witnesses, because of the sad history of racist violence in America. I don’t know which version of the story is true. Both sides sound fairly plausible.
Given the widely varying witness statements, it was understandable to decide not to indict (though it probably could have gone either way). From the prosecutor’s point of view, I don’t want to indict unless I think the person is actually guilty and deserves to be punished.
There are riots because in many people’s minds the decision not to indict is a judgment that what Wilson did was right, and sends a message that police can kill young black men even without a good reason (as they certainly have before) and get away with it. Rioting has long been a way in which people vent their anger and frustration. Of course it doesn’t make much sense, and hurts the community (though sometimes such events might inspire authorities to enact new policies that improve the situation on the ground.)