You will need the Limited Read People permission to see this information.
Navigate to the person's profile and click on the "Involvement" tab. Then select the "Groups" sub tab. All groups the person is currently a member of will appear grouped by the group category. Groups without a category will appear under the "Uncategorized" section.
You can use the "Effective Date" field to filter the groups based on which groups the person was a member of on that specific date. If no date is specified, all current and past groups will show. The active date range of the person's membership is shown to the right of the group name.
You can click on an individual group to expand and view details of the person's membership in that group. You can also hover over a group category and use the "expand all" and "collapse all" to show all or hide all groups in the section respectively.
The fields that appear under a group are all the custom fields defined on a group membership profile (if any).
The following actions are available.
You must have the Write Full Groups permission to perform these actions.
Edit - edits information related to the person's membership within the group.
Remove - completely removes this person from the group. If you would rather drop them and keep history, edit the record instead and add a drop date.