The core principle on which the Declaration of Independence is based is that government is based on the just consent of the governed.
This doesn't sound like a particularly radical principle in this day and age, but at the time in which the Declaration was written, it most certainly was. Most governments at that time paid little or no attention to the consent of the governed—the ordinary people, as it were. They were there to serve the interests of those in charge and acted accordingly. One can see, then, why the Declaration's core principle was so radical for its day.
But the Declaration of Independence goes even further than this. Not only is government based on the just consent of the governed, but it depends for its continued existence on its ability to deliver certain goods, namely life, liberty, and the pursuit of happiness. And if governments are unwilling or unable to deliver such goods then the people—"We, the People"—have the right to get rid of the government and replace it with one that will.
This is another principle radical for its time. In those days, most governments regarded themselves as having been instituted since time immemorial and believed that it was therefore dangerous—and in some cases even blasphemous—for the people to remove them.