Minnie's peers are other women--those who understand the pressures of having to take whatever the man dishes out, so to speak. Specifically, they are Martha Hale and Mrs. Peters.
Martha knew Minnie as a girl, so she is clearly older than Minnie and is therefore not particularly her peer because of age. Mrs. Peters is the Sheriff's wife, a position much higher than that of Minnie, so she's not really Minnie's peer on a social level. However, both are women who understand what happened in this relationship and what happened to Minnie to cause her to commit such a drastic act of violence against her husband. That's what makes them her peers.
Their dilemma in "A Jury of her Peers" is whether or not to tell what they've observed, which is obviously more of a problem for the wife of a sheriff than for a fellow farm wife. What they decide, in their unspoken jury deliberations, is that the men who are investigating would probably not believe them, and the men on the jury would probably convict her (without any real understanding of her circumstances) if they did hear all the evidence. Thus, Minnie's jury of peers conducted a trial, and they found her innocent.