Documentation has been added to the wiki about properties.schema and how to create them: Properties Schema and Schema Input Types and Validators 

properties.schema is a file that the authoring tool uses to construct a configuration interface for a plug-in. Without it, you wouldn't be able to assign an image to a Graphic component or vary the number of items in an accordion. In order to be compatible with the authoring tool, a plug-in (component, extension, theme, menu) must have a properties.schema when it is uploaded to the authoring tool.

Wiki documentation is always a work in progress. Please feel free to expand and to correct it.

Because this documentation is available for reference, this thread might be a natural place to ask questions if you're a developer who is struggling with a schema issue.