Subject headings are a formalized way of of searching library catalogs. The right subect heading can help you get to information more quickly.
For example, the American Revolutionary War can be described using the following terms
American Revolution
American Revolutionary War
War of the American Revolution
American War of Independence
War of American Independence
War of Independence
You could search the library catalog for all those words. Or, use one subject heading to find all of the library's materials about the the American Revolutionary War:
Nordamerikanischer Unabhängigkeitskrieg
Find books on your topic by using a keyword search to find relevant subject headings. For example, search the keyword "Nordamerikanischer Unabhängigkeitskrieg", in the library catalog. By clicking on one of the keywords for the first book, Die amerikanische Revolution, the subject headings lead to other relevant books on this topic.