AOA is Alpha Omega Alpha, the honors medical society. It's a good thing to have on the residency application. The number of people who get elected is maxed out at 1/6 of the graduating class (I think).
Each chapter has slightly different election criteria, but more or less they accept the top academic students in each class. At my school, Junior AOA is selected based on Year 1 and 2 test scores. Senior AOA criteria are a little more broad and include clerkship honors as well as taking into account extra-curriculars. I think Step 1 scores are a non-factor at my school.
As for what the members actually do, I haven't seen much out of the chapter here. Pretty low profile. I know they put on a residency information session and publish a residency application guide. I think they have a hand in organizing the annual residency fair too.