Library of Congress Subject Headings (LCSH) are assigned, perhaps unsurprisingly, by the Library of Congress. For more about Library of Congress Subject Headings click here.
For our immediate purposes, subject headings are useful in same way that categories are when shopping for something online: subject headings get you exactly want you want. Every single book published is assigned subject headings by catalogers, so that if you click on a subject heading in a computer catalog it will pull up every other book that has been tagged in the same way. Rather than throwing words into a search and hoping for the best, subject headings allow you find materials that are related to your topic but not be using the same words you are. Using subject headings will greatly increase the depth of your search and ensure that your literature search is complete.
In the case of this subject heading:
Indians of North America -- Government relations
The main subject heading is "Indians of North America" and the subheading, the more specific topic, is "Government relations." If you click on this subject heading in the catalog, or type it in from scratch by going to advanced search and picking "Subject" from the drop down you will see that there are a little over one thousand books in the library sharing this subject heading.
Library of Congress Subject headings are a controlled language, meaning everyone has to use the same terms if they are going to work everywhere. Some people might prefer the subject heading "Native Americans of North America" or "American Indians of North America" or "Indigenous Peoples of North America" but, for now, the Library of Congress has decided that every library in the United States will use the subject term "Indians of North America" at this time.