The Blighters are the Templar-run gang that controls London in 1868 and the enemy you fight in almost every street, stronghold and gang war in Syndicate. Maxwell Roth built the gang for Crawford Starrick, and a Templar lieutenant runs each of the seven boroughs.
They extort businesses, kill anyone who resists and run factories on child labour. They began in Devil's Acre, the worst slum in Westminster, and spread across the city until only Whitechapel's Clinkers stood against them.
You take each borough back by freeing child labourers, clearing strongholds, removing their Templar agents and finally beating the leader in open gang war. Blighters defect to the Rooks as you gain ground, and the Notoriety upgrade stops them starting street fights with you.
All seven leaders die in gang wars led by the twins. Jacob kills Roth in a fire at the Alhambra in Final Act, and the twins kill Starrick in the Buckingham Palace vault in A Night to Remember. By the end of 1868 the Blighters are finished.