The 'story' template in t4 is used for news or events story items. Typically you'll create a new section called 'News' or 'Events' and fill it with news stories or different event details.

It's important to include summaries and summary images when you enter your news stories using the story template:

The feed that is generated by a section using 'story' content can be pulled into a tile showing the headlines for any news or events.  Like other tiles, you can change the tile colour scheme using the option at the bottom of the editor: