What was the importance of the insular cases?

The Insular Cases made the distinction between "Incorporated" territories like Hawaii and Alaska (where full US sovereignty had been established), and "unincorporated" territories (like Puerto Rico and the Philippines) which came into US hands through war, but which were not claimed as sovereign territory.

The Court said that the Constitution applies totally in the incorporated areas, and only partially (meaning: basic due process rights) in the unincorporated.