The Brotherhood was a mutant terrorist organization that had ties to the Hellfire Club.
After the Purifiers drove her away from Clark County, Blink found other like-minded mutants who were fighting against mutant persecution. These mutants were members of the Brotherhood, and although Blink did not join their ranks, she helped them out with some of their operations. When they tried to get her to do things that she was not willing to comply with, Blink cut her ties with the Brotherhood. 
By 2017, the existence of the Brotherhood was unknown to the Mutant Underground.  Before disappearing, the Brotherhood left behind considerable wealth and resources to the modern day Hellfire Club.