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The Edit My Reports permission
The Edit My Reports permission requires Create and Customize Report permission too. This permission allows the user to edit, move, save, and delete a report created by that user (not created by other users) in shared folders.
When the user has access to a report folder, the user is able to store a new report to a report folder; even user accessibility to the report folder is only as Viewer. The user will also able to edit and delete reports created by that user in the public report folder, with the user access is Viewer.
Without this permission, if user access to the report folder is Viewer, the user will not be able to overwrite a report stored in the public folder even if the report is created by that user. This scenario will be only possible when the report is moved by someone from a folder who has Editor access to other folders where the user has Viewer access only.
As with the View Reports in Public Folders permission, this permission should not be given to everyone. It allows the user to store reports to any public report folder where the user has access, even only as Viewer.