A vigilante is a private individual who legally or illegally punishes an alleged lawbreaker, or participates in a group which metes out extralegal punishment

Punishment

Punishment is the authoritative imposition of something negative or unpleasant on a person or animal in response to behavior deemed wrong by an individual or group....

 to an alleged lawbreaker.

Members of neighborhood watch

Neighborhood watch

A neighborhood watch or neighbourhood watch , also called a crime watch or neighborhood crime watch, is an organized group of citizens devoted to crime and vandalism prevention within a neighborhood...

 programs and others who use legal means of bringing people to justice are not considered vigilantes. For example, in 1979 Curtis Sliwa

Curtis Sliwa

Curtis Sliwa is an American anti-crime activist, founder and CEO of the Guardian Angels, and radio talk show host and media personality.-Guardian Angels:...

 founded the Guardian Angels

Guardian Angels

The Guardian Angels is a non-profit international volunteer organization of unarmed citizen crime patrollers. The Guardian Angels organization was founded February 13, 1979 in New York City by Curtis Sliwa and has chapters in 15 countries and 144 cities around the world.Sliwa originally created the...

 in New York City

New York City

New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...

, a recognized crime fighting organization that now has chapters in many other cities.
Spanish for watchman, guard, from vigilante vigilant, from Latin vigilant-, vigilans
.

Note that the term vigilanties is a derivative of vigilante, that derives from vigilant, like the word vigilance.