The Enlightenment was, perhaps, one of the most influential movements of modern Westten society. The topic itself encompasses a wide expanse of thinkers and philosophers, and connections can be drawn between the Enlightenment and the Scientific Revolution, as well as the Renaissance in Western and Northern Europe.
That being said, the Enlightenment revolutionized the way in which citizens viewed their respective governments. Western democracy still displays many aspects of this change that was brought about by thinkers such as John Locke, Jean Jacques Rousseau, Thomas Hobbes, Baron de Montesquieu and Voltaire. One of the more revolutionary ideas was the concept of a social contract that exists between the government and the governed. Ironically, while many of these thinkers promoted the notion of a social contract, their reasons for doing so were not always for promoting the ideals of democracy. In some instances, as with Thomas Hobbes, the social contract was introduced as an argument against democratic government.
Regardless, the social contract suggested that there was in fact a contract between the government and the governed, whereby the governed forfeited some of their rights in exchange for the protections and stability government provided. In instances, where this contract was ignored, the impacted party had a right to seek an alternative. The U.S. Declaration of Independence references this concept- “That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness” [sic].
Additionally, Enlightenment thinkers believed that all humans were entitled to natural, god-given rights. John Locke is one of the more famous advocates of these rights, arguing that men are entitled to the life, liberty and the pursuit of property. Thomas Jefferson immortalized these ideas by their inclusion in the U.S. Declaration of Independence, replacing “property” with “the pursuit of happiness”.
In examining the American Revolution and the French Revolution if the 18th Century, one sees the influence the ideas of the Enlightenment has on society. While the ideas of John Locke seemingly formed the foundation of both revolutions, the ideas of other thinkers became ingrained in the ensuing governments, most notably in the United States Constitution. For example, the notion of separation of powers that is inherent in the U.S. political system was an idea proposed by Montesquieu in his work The Spirit of the Laws. Many of the rights afforded in the U.S. Bill of Rights (freedom of religion; freedom of speech) were ideas proposed by the French writer Voltaire.b
It is important to note that while the Enlightenment seems like a time citizens seemed to demand much from their governments, there was a similar onus placed on citizens as well. Again, there was the idea of a social contract. As in any contract, both sides were expected to honor their end of the agreement. Citizens, therefore, had a responsibility to their government as well as responsibility to speak out against any shortcomings of their government.
The Enlightenment was a heavily influential time period, but it should be noted that the Enlightenment is a big topic and is made up of many thinkers of profound historical significance, each of whom tended to say very different things from one another. This makes tackling the totality of your questions in such a short format practically impossible. This is one area where you really would need an entire book. Still, I'll give my thoughts as to a few of the notable trends running within the Enlightenment which have proved particularly influential in shaping later centuries of political discourse.
Among the most ubiquitous hallmarks of Enlightenment era political thought is the notion of the Social Contract. First postulated by Thomas Hobbes in defense of Absolutism, then taken up by John Locke to attack Absolutism, and later still by Jean Jacques Rousseau, Social Contract Theory states that governments were originally created to serve a function, and its adherents spent tremendous energy trying to discern what that original function was (this is the so called "Social Contract"). Some of their conclusions, particularly those of Locke, have been very influential in shaping modern values concerning governmental authority and political freedom.
For Locke, governments exist to safeguard the essential freedoms of life, liberty and property, and therefore any government which becomes oppressive loses its legitimacy. In such cases, resistance becomes a valid response to tyranny. This logic would serve as the theoretical underpinnings of the American Revolution, and its underlying assumption—that governments have a responsibility to safeguard the rights of its citizens—has not really gone away. That being said, modern democratic thought has changed and further evolved over time, particularly with the added influence of nineteenth-century Liberalism and Utilitarianism.
Similarly, the Enlightenment has been profound in shaping the discourse around political rights. Notice that political rights, like laws, tend to be listed and codified. With this in mind, the 1689 English Bill of Rights becomes a kind of turning point: it provided an explicit list of rights that would be protected and guaranteed to all English citizens. In the following century, the American Bill of Rights and the French Declaration of the Rights of Man and Citizen would follow. Collectively, these documents have established a precedent which still holds tremendous influence today and serves as the foundation from which our modern understanding of political rights come from.
Finally, the Enlightenment era thinkers did tend to expect and advocate for a high degree of individual and collective responsibility. Lockean political ethics fails if the people lack the willingness to resist arbitrary rule. When Voltaire was writing against political abuses, he was working to challenge real injustices, and he did so by publishing. The Enlightenment was highly literate and discursive, and if its adherents simultaneously made appeals to the reading public, they also expected to heard by that reading public.