Purpose of Government

What is the purpose of a government? Why does a government need to exist? An oversimplified answer would be - 'to serve the people'. For a deeper explanation, that identifies the complexities involved, read further.
"We hold these Truths to be self-evident, that all Men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty, and the Pursuit of Happiness -- That to secure these Rights, Governments are instituted among Men..."