The Gyōja (行者, ぎょうじゃ, "Ascetic") are the orphans raised by Goryōmaru trained to be demon hunters after the parents of the children were killed by demons. They killed demons and took their bodies to their master.
Despite how they want to help people by slaying demons, they apparently attack any random demon indiscrimantly, as they killed both innocent and evil. They would even go as far as to attack humans in order to achieve their goal; this was shown when they had threatened to kill Kagome if she stood in their way when their target was Inuyasha.
The Gyōja in the manga.
However, despite their irresponsible intentions, it was later revealed that the children were simply undisciplined as their master, Goryōmaru, was against slaying innocent demons.
When Inuyasha and the gang discovered that Gakusanjin was killed by the Gyōja, they decide to investigate the Gyōja. Gyōja attacks them while Inuyasha and his friends on a break, but they were no match for Inuyasha as they runs off. They follow the Gyōja to their temple. Gyōja were scared of the hordes of demons comes, and after Goryōmaru defeats them with his demon arm that there's too many, they were surprised that Inuyasha use the Kaze no Kizu with the Tessaiga, then Sango use the Hiraikotsu and they're amazed as Miroku use the Kazaana to suck all the demons. After their master's death, the boys are sent by Inuyasha's crew to a nearby village to be taken care of.