I agree with the above post on the significance of the Enlightenment; but the argument on the Great Awakening seems less sound at best. The Enlightenment was important in that it emphasized the basic worth of human beings. Among the great Enlightenment thinkers, Montesquieu argued for a separation of powers within the government; and John Locke argued for government by the consent of the governed. More importantly, Benjamin Franklin and Thomas Jefferson were both Enlightenment thinkers. Both were deists and opposed the domination of the church in politics; in fact Jefferson made no reference to God in his original draft of the Declaration of Independence; it was added later over his objection. It is noteworthy that Jefferson relied heavily on Locke's Second Treatise on Civil Government in the Declaration of Independence:
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, --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
The influence of the Great Awakening was indirect at best. It should perhaps be noted that the religious revival of the Awakening was in large part a reaction and response to "rationalism" of the Enlightenment. There was no sudden realization that people should have their own ideas about government because they now had their own ideas about God. Rather the First Great Awakening saw the founding of a number of colleges and universities, such as Princeton, Columbia, Brown and Rutgers. (These were the first of the "Ivy League" schools because there were four of them, in Roman numerals "IV.") Although founded for the purpose of educating ministers, they also educated a number of independent thinkers who were instrumental in the revolution. Interestingly, and ironically, Aaron Burr, a colonial in the Revolutionary Army more famous for killing Alexander Hamilton was the grandson of the great Jonathan Edwards, one of the foremost Great Awakening ministers.
These events were extremely important in creating the American Revolution because they both made people much more likely to support the idea of democracy.
Thinkers of the Enlightenment argued that the only rational form of government was one in which the people consented to be ruled by a government. There was no reason, they said, to accept the idea that some man (the King) deserved to rule because of who his ancestors had been rulers. This was obviously a democratic idea.
The Great Awakening was also democratic. This was because it promoted the idea that people should be able to have their own relationship with God rather than doing what church officials told them to do. If people were good enough to have their own ideas about God, they should also be able to have their own ideas about government.
In these ways, these events helped to promote the idea of democracy and helped to create the American Revolution.