Subthemes allow a designer to create variations to the main theme (template) that may be more appropriate for some pages. In practice, subthemes typically differ from the main (default) theme by adding or removing columns.
A subtheme may be applied to a page when editing it by choosing a 'Theme Variation', which lists all the available subthemes for the current theme. You may also use 'action maps' to have the system automatically select a subtheme for a particular module/view. Subthemes are specific to a theme and are referenced by their name, so a particular subtheme may not be available when switching themes. However, Exponent defaults back to the default theme template (index.php) whenever it cannot find the specified subtheme, so the pages will still be shown.
Subtheme template files are stored in the 'subthemes' folder inside your theme's folder. It's sometimes easier to create a subtheme template by making a copy of the main theme template 'index.php', renaming it, placing it in the 'subthemes' folder, and then editing it.
It is recommended to keep the main (default) theme template (index.php) generic as it will be used by default. Meaning, most non-pages will be displayed using either the default theme template or trying to follow the parent subtheme (which isn't always possible). Therefore, if you have a very busy home page (template), you might want to make that as a subtheme and use the simplified varation as the default template.
The format for a subtheme template is identical to the main theme template