The term Illuminati is thrown around loosely these days in books, movies, and video games. The real Illuminati, however, can be classified by their two roles; that of the past and that of today.
The Bavarian Illuminati were founded by Adam Weishaupt in 1776. This movement can be described as an offshoot of sorts from the free-thinkers of the Enlightenment in Europe at that time. The members, which had reached over 10,000 Europe wide within 10 years, planned to infiltrate and overthrow the numerous European States of the time. The goal was to have Illuminati members in power as puppet rulers so that the Illuminati higher-ups could actually dictate the real actions. This plan never came to fruition as secret-societies were outlawed at that time.
The modern Illuminati is a little bit more tricky to pin-point. No-one has ever publicly acknowledged a secret society forming around the early ideas and principles of Adam Weishaupt but many conspiracy theorists believe that there is a group operating worldwide in the background. These 'men behind the curtain' dictate governmental actions all over the world. They aren't just politicians, but businessmen, intellectuals, financial barons, military minds and the like.
The problem here is not a group of people meeting. It is the power of ideas, and Adam Weishaupt's ideas told of an association or order that would eventually come to govern the world; the main goal of which was to banish religion and overturn civil governments. He tried to make these dangerous ideas sound a little less harmless by camouflaging them. Who would fight the idea of a nicer, better world where we were all unified. Such an idea was sure noble.
Adam Weishaupt wanted a new way for the world. A new world order.