Answer:
It asserts that Americans as a whole (and not as members of their respective colonies) are a distinct “people.” To “dissolve the political bands” revokes the “social compact” that existed between the Americans and the rest of “the People” of the British commonwealth, reinstates the “state of nature” between Americans and the government of Great Britain, and makes “the Laws of Nature” the standard by which this dissolution and whatever government is to follow are judged. “Declare the causes” indicates they are publicly stating the reasons and justifying their actions rather than acting as thieves in the night. The Declaration is like the indictment of a criminal that states the basis of his criminality. But the ultimate judge of the rightness of their cause will be God, which is why the revolutionaries spoke of an “appeal to heaven”—an expression commonly found on revolutionary banners and flags. As British political theorist John Locke wrote: “The people have no other remedy in this, as in all other cases where they have no judge on earth, but to appeal to heaven.” The reference to a “decent respect to the opinions of mankind” might be viewed as a kind of an international public opinion test. Or perhaps the emphasis is on the word “respect,” recognizing the obligation to provide the rest of the world with an explanation they can evaluate for themselves.