In the Declaration of Independence, Jefferson claims that Governments are instituted among men to secure their God-given unalienable rights, with the consent of the governed. When a government becomes destructive to this, it is the right and duty of men to take it down and establish a new one that fulfill the mentioned purpose.
These claims impact his overall argument because he is trying to prove that the English government of the thirteen colonies doesn't fulfill its duties anymore, so they are entitled to break away from it.