Is society a contract and does it matter?

In an election year, when Americans are in the grip of policy debates and heated discussions as to first principles, the question as to whether society is a contract requires particular attention. This is because our views on social contract theory not only shape our political predilections, but also because they have a direct impact on our views with respect to culture, family, and work.
What is a social contract, and, moreover, why does it command such importance?