Structure lets you group by most standard Jira fields, custom fields provided by Jira and other issue attributes:
The fields that cannot be grouped by are dates and numbers.
Groups can be nested. For example you can take a list of issues and group them by fixVersion and then by Assignee. Thus you will see the existing fixVersions on the top level, Assignees on the second and then the issues themselves on the third, grouped accordingly.
If you enable editing via Structure in the generator settings, Structure can update the fields by which the issues are grouped when you drag-and-drop issues from one group to another.
Updating a field may not always be possible. For example, Status field can be updated only if the update is allowed by the workflow and there are no required fields or dialogs to show. If the update made via drag-and-drop fails, the structure will return to the previous state (the issue will jump back).