The functionality is described here:

Though at least in v0.5.2.374, it only launches the app and triggers some kind of search which doesn't yield any results.

Hopefully, it will at some point work again so that it's possible to use the Spotify URIs described in the blogpost to launch tracks, show playlists, etc.

Application homepage:
iTunes link:
HTML Link example:
Native application URL string example: spotify:track:0FMhMAFPLg8EljnROSoVnj
Extended example: