If you’re a vigilante, you might take the law into your own hands by trying to catch or punish someone in your own way. If you wrestle jaywalkers down to the ground, you might be called a vigilante.
Vigilante is a form of the word "vigilant," which means keeping a watchful or close eye on events and people. Sometimes a vigilante will make news for catching a criminal, and sometimes vigilante groups form to target crimes in a bad neighborhood. A common combined use is "vigilante justice," meaning a form of law-keeping outside of the official channels of police and the courts.