Style file must be named according to your actions shortname. Its a json file, which includes css-like styles.
While all other directories can be found both in the main level and theme, the styles directory belongs only to the action’s theme. It’s setup like this to avoid confusions with style inheritance and overriding. Note that your application will have styles also from other actions, from components, built-in styles and application’s main style definitions. Hence it is recommended to use style naming which is specific to your action to avoid collisions.
Please see the documentation for styles here:
http://docs.appzio.com/toolkit-section/styles-components/