Operating systems give native applications a way to register their ability to handle files with given MIME types and/or file extensions. This has many use cases. An image editor might be able to display and edit a number of image formats. A movie player might understand a video format. A data visualizer might generate graphs from .CSV files. A Logo environment might interactively step through Logo programs.
Typically, the application might be activated when the user double clicks on a file, or right clicks on the file and chooses the application from a context menu.
Installed Web Applications should be able to have the same capability. They could use the manifest to declare which file types they handle, and receive a service worker event when activated. The explainer has more details.