This line of text in the DOC refers to Natural Rights, an idea originally imposed by John Locke -- one of the famous Enlightenment thinkers.
Natural Rights are rights that all men/women are entitled to -- meaning they can't be taken away by any kings or dictators.
When most people think natural rights they also think: Life, Liberty, and Property. In the DOC, this was changed to "Life, Liberty, and The Pursuit of Happiness.