Vigilantes are people who voluntarily carry out duties usually done by heroes without paying attention to the law. Due to the hero regulations, people are not allowed to carry heroic duties out on their own and vigilantism is therefore forbidden.
The origins of heroes can be traced back to the vigilantes. When Quirks started to manifest there was no organization that controlled the pro heroes and they were therefore vigilantes. The Pro Hero System was first put into place on Rhode Island in America under the "Rhode Island New State Statute", 189 Vigilantes were affected by this statute, with only 7 being accepted as official Heroes. Nowadays most of the vigilantes have vanished.
However, Knuckleduster, Pop Step, and The Crawler had been regularly active in their activities to help people and dispense justice as vigilantes. Aizawa stated that the pro heroes had never taken action against them and left those three be so long they do not abuse their Quirks and go on a rampage.