Spotify is a well established music streaming service, that allows you to build up a library which you can play any time on any device (assuming you use a premium account). However, Spotify's music library does not include every music track you could ever want to hear. In such cases, the Spotify Desktop application lets you include local files (which you may have bought elsewhere) into your library. But these also only exist locally.
If you use multiple devices, this is a little bit of an inconvenience. Of course it would be best, if you have your complete music library accessible everywhere. But the good news is: you can keep your music library consistent on multiple devices, if you simply synchronize these additonal files with your desktop devices manually.