In many ways the Enlightenment never ended. The secular commitment to rationalism (the idea that human reason is the primary, or the only, path to truth) has persisted, and while it may have manifested itself in seemingly irrational ways, even relativists and postmodernists are rationalists. Relativism, in fact, is one of the best-known offspring of Enlightenment rationalism; moral and religious authority began to devolve from any Divine source and centered on the now-deified human reason, meaning that right and wrong became human constructs, not absolute truths revealed from on high.
We've been wallowing in the muck of meaninglessness ever since. A lot of historians claim the Enlightenment began in the 17th century, but its roots were much deeper—during the Renaissance thinkers began formulating the ideas that would become rationalism, and even further back the Greek philosophers used observation and conjecture (not divine authority) as their basis for acquiring knowledge. It can't be disputed, however, that the 18th century was the fluorishing period of Enlightenment thought.
This is the time period in which the modern world began to take shape. It's hard to say who it all started with (Descartes is usually a front-runner for that distinction), but Rousseau became the poster-child of the movement with his theories of man as a "noble savage," best left in his natural condition and ultimately corrupted by civilization, and the corrolary (and, as any child can see, completely incompatible) idea that it is the State and Education which can save mankind from his culture-induced wickedness and ignorance.
Lack of knowledge, therefore, was seen as the source of mankind's ills. It was not intelligence that would solve the problem, however, but mere acquisition of information. So a bunch of Frenchmen, intoxicated by this concept, set about compiling a compendium of all knowledge lodged in the collective human conciousness. They called it the Encyclopedia, though they could just as accurately have called it the Internet. Yes, you read that correctly: the intention of the Encyclopedists was to put all of human knowledge in one place.
Who would be influenced by these guys? you may well ask. Pretty much everybody. Human Reason was lifted above Divine Revelation, and the age of godlessness was inaugurated. Literature of the period took a serious turn for the irreverant and/or highly abstruse, though Practicality was everywhere touted as the primary aim of true intellectuals. Satire became a preferred model for intelligent fiction, with men like Voltaire, Henry Fielding, and Tobias Smollett leading the way.
On the political front, fairly well-known works began to surface, among them Thomas Paine's Common Sense, the Constitution of the United States of America, and Adam Smith's The Wealth of Nations. The world has never recovered. The proposition that man is capable of governing himself at first produced a highly-functional republic in the newly-formed United States, while simultaneously laying the foundation for the current attitude which privileges "democracy" above all else and relegates republicanism to a less-evolved status in our nation's growth.
It wasn't all bad. Brilliance often accompanies shoddy thinking (or antichristian thinking, as the case may be), and while many of the Enlightenment authors were way off-base from a Christian perspective, their books and poems and essays make great reading. Voltaire wrought a lot of damage on the West's intellectual tradition, but it's pretty hard to argue that Candide is the work of anyone less than a genius. Ben Franklin, Jonathan Swift, Lawrence Sterne, Alexander Pope—mostly off-base, but some of the best writers the world has ever known.
We encourage the study of 18th century literature be approached with caution. The old Christian humanism of the Renaissance was replaced with a new creature called secular humanism, and the effects were chaotic and largely destructive. Still, this is literature that can't be ignored, especially not by any Christian who really wants to understand exactly what's going on in the world these days. It's also pretty fun, and while the Enlightenment philosophy poses clear dangers, it also motivated many writers to show what fine form man is capable of.