As time went on, the Scourers became increasingly corrupt. Far away from the jurisdiction of their native magical governments, many indulged a love of authority and cruelty unjustified by their mission. Such Scourers enjoyed bloodshed and torture, and even went so far as trafficking their fellow wizards.
-- from the History of Magic in North America (Pm)
17th century – Rogue band of vengeful mercenary wizards who caused a huge problem between wizards and No-Majs.
During the early years of the European Wizarding community in America, there was no government or laws. As a result, unscrupulous bands of wizards formed mercenary bands to enforce their brand of justice. They were bounty hunters who would search for not only outlaws and criminals but also any witch or wizard for whom someone was willing to pay gold. Over the years in the late 1600s, the Scourers became feared for the brutal, dangerous groups that they were. They were not above capturing and accusing innocent No-Majs as magical in order to collect bounties during the years of witch hysteria.
During the Salem Witch Trials of 1692-93, two of the Puritan judges were actually Scourers settling the score in feuds with fellow Wizards.
"scour" - scrub clean
Scourer is a real dictionary word with two meanings - one, someone who scours or cleans or purges [http://www.merriam-webster.
Since JKR used the word "mercenaries" the scourers would have started off as soldiers of fortune - fighting for whomever paid them. Then they evolved into bounty hunters - probably because the skillset was transferable. And a couple of them even became judges - those who got to decide who was guilty of witchcraft and who wasn't - what influenced said decisions is only hinted at. We know that they were generally motivated by money, but all we know for sure is that they were known to use their position to settle old scores.
Two reasons are given for scourers teaching their descendants that magic is real (ie recognizing the signs) and evil - vengeance and avoiding discovery. If the scourers were discovered, they would be charged and sentenced - so they did have something legitimately to fear from the presence of magic. -vaml