Sharing experiences among people from the same group (women in math, black people in STEM, LGBTQ people in CS, etc) can be a very powerful tool: it can build community; make people feel less isolated and realize they are not the only ones facing these challenges; help people trade advice, tools, help; start some mentoring.
This could also lead to the sharing of such experiences with the greater community (for example, the whole department or university), which might help find allies, build a greater supportive community, and enlighten others as to what it might be like to be from that group. Something else that can be useful sometimes is for people from that group to realize that some of their struggles are also shared by people from the majority. For example, many students might actually feel some professor is rude to them, which could mean the professor is not racist or sexist, simply rude. This is not to say that sexism or racism do not exist! But it can be very isolating for someone to feel they are the only one with that struggle, so finding others who share that struggle can help a lot.
Before (or as you are) asking for people to share their experience, you can show them these few links which might be helpful in making you all reflect on or notice experiences you may have had. Maybe similar things exist related to your own institution, discipline, etc?
-- Gender microaggressions at Harvard in STEM. Try out the Pipeline game mentioned in the top post too! http://genderinharvardstem.tumblr.com/
-- At Stanford: https://femtastic.wordpress.com/category/women-in-stem/
-- I know various women in math conferences (or even general math conferences) will often have panels or discussions or some other way to encourage participants to share their experiences, and many of my colleagues have found this very empowering, so keep an eye out! You should never feel obligated to share anything though! For some people, just listening to others is helpful.
Here are some sample questions you could ask participants in a discussion or survey, and an opening, feel free to use them or modify them as you wish!