I was in a sorority in undergrad and was extensively involved, was president for a while and board member the rest of the time.
At the end of the interview for the med school where I am currently, the interviewer asked me for an "impressive" fact. We ended up talking about my role in the sorority, a specific conference that we organized, and how it was kind of a watershed moment in my personal development. Obviously my resume has more typical "premed" things, but this particular experience was a big portion of that interview and it seems like that faculty member played a big role in my getting admitted.
I probably wouldn't have thought it relevant if it was just a social activity or a club that I belonged to, but for me my sorority was a community that yielded friendships, support, and opportunities. I think it just depends on what the organization is to you, like anything else in your app.