My observations so far with the Host button is that it is used to somehow Sync the DAW to the Spark UI. For example, if I press Play in my DAW with the Host button lit, the Spark will begin to play too. However, if I turn Host off, it will no longer share a reaction.
The "Tempo" button is apparently used to sync the Spark tempo to the DAW. Changing the tempo in my host application will increase the tempo in Spark even if the host light is not lit.
I guess the breakdown is that Tempo is a direct Sync to the Host DAW Tempo, whereas Host provides a general interface sync to the transport functions.
Hope that helps someone else out there some day. Anyone who has more experience and can really get to the details about the Host button, feel free to chime in!