This phrase, found in the closing paragraph of the Declaration of Independence, refers to "all political connection" between the American colonies (which became states with the Declaration) and Great Britain. In other words, from the perspective of the signers, the split became complete with this statement. By claiming to end all political connection, they proclaimed the right, as a collection of sovereign states to make war, come up with their own governments, conclude treaties, and enter into alliances with foreign powers. Jefferson spends most of the Declaration building a case for independence by citing natural law and enumerating the abuses of the Crown. In the final paragraph, he "gets to the point," if you will, by declaring that the colonies are independent. The United States of America (a new phrase in its own right) were "absolved of any allegiance to the Crown," and would dictate their own future independent of Great Britain, if they could back up their declaration with victory in the Revolutionary War.