The statement "We the People" represents a form of democracy. Showing that normal people (civilians) are the power of a nation, which in other words is a democracy. What the statement really means is that the ordinary people of the nation, are the ones that decide how the nation will live and thrive, instead of being governed by a higher position (like a king for example). This is what happened when the First American Colonies decided to break away from Great Britain back on July 4th 1776, which is how we came to the US holiday dubbed Independence Day.
Hope this helps.
-Northstar