Jabberwock is a loosely associated network of activists and hacktivists that identify themselves as Inhuman. Their goal is to prevent discrimination against and protect inhumans from enemies they believe want to return to the "old ways". They employee numerous techniques to achieve their goals and will often "out" a discriminator or criminal preying upon inhumans to public shame and scrutiny.
Over the last fifteen years, Jabberwock has revealed numerous instances of Inhuman discrimination and crimes committed against them. The FBI doesn't believe that most members are, in fact, Inhuman due to the number of members in the U.S., alone. The group has also been instrumental in helping and protecting Inhumans it deems worthy.
There doesn't appear to be any central leadership and which Inhumans or which criminal are targeted appears to hinge on the sympathy or anger from a certain percentage of the membership.