Jefferson is relying on Enlightenment thinking, especially that of John Locke, in asserting the Laws of Nature (also called Natural Law) in support of American independence from Great Britain.
Jefferson is arguing that all people (he sees "people" as white males) have a natural right, granted to them by God, to life, liberty, and the pursuit of happiness. Because Natural Law guarantees this, the relationship between the ruled and a ruler becomes a contract, based on the consent of the governed. If the ruler becomes a tyrant, interfering with the Laws of Nature that allow men freedom and happiness, that ruler can be legitimately overthrown.
This is much different from medieval and Renaissance concepts of the relationship between the ruler and the ruled. Under the ideology of the Great Chain of Being, a ruler is appointed by God. The people have no say in this appointment and must obey. If a ruler turns out to be a tyrant, that is God's will: God has clearly sent the monarch as an "iron rod" to punish the people. The people simply have to go along with this.
Jefferson is saying, in contrast, that the people have a say in their governance and a natural, God-given right to reject tyranny. Much of the rest of the Declaration of Independence will outline the abuses of George III. In laying out this argument, Jefferson is doing his best to legitimize the revolution, especially in the eyes of fellow colonists who might have had doubts about breaking from England.