Illuminati (plural of Latin illuminatus, "enlightened") is a name that refers to several groups, both historical and modern, and both real and fictitious.
Historically, it refers specifically to the Bavarian Illuminati, an Enlightenment-era secret society founded on May 1, 1776.
In modern times it is also used to refer to a purported conspiratorial organization which acts as a shadowy "power behind the throne", allegedly controlling world affairs through present day governments and corporations, usually as a modern incarnation or continuation of the Bavarian Illuminati.
In this context, Illuminati is often used in reference to a New World Order (NWO). Many conspiracy theorists believe the Illuminati are the masterminds behind events that will lead to the establishment of such a New World Order.
Confusing the issue further is the fact that there are also several modern fraternal groups which include the word "Illuminati" in their names.