The Illuminati (or Moriah Conquering Wind as they prefer to call themselves these days) is a very secretive group of occult practitioners who have been around for thousands and thousands of years. It is not a boys' club or a group of adult parents trying to get some excitement in life; this is something much bigger than that. This is a very well structured organization consisting of people in extremely High Places. Those people are the Super Wealthy, who stand above the law. Many of them don't even appear on the list of the wealthiest people in the world - it's that secret.
The word Illuminati means 1. People claiming to be unusually enlightened with regard to a subject. 
2. Various groups claiming special religious enlightenment. Latin illuminati, from pl. of illuminatus, past participle of illuminare, to light up. See illuminate. These definitions are taken from "The American Heritage Dictionary of the English Language". 
Those people are the top players on the International playground, basically belonging to the thirteen of the wealthiest families in the world, and they are the men who really rule the world from behind the scene (yes, they are mostly men, with a few exceptions). They are the "Black Nobility", the Decision Makers, who make up the rules for presidents and governments to follow, and they are often held from public scrutiny, as their action can't stand being scrutinized. Their bloodlines go back thousands and thousands of years, and they are very careful with keeping those bloodlines pure from generation to generation. The only way to do so is by interbreeding. 

Their power lies in the occult and in economy - money creates power. The Illuminati own all the International banks, the oil-businesses, the most powerful businesses of industry and trade, they infiltrate politics and they own most governments - or at least control them. An example of this is the American election for presidency. It is no secret that the candidate who gets the most sponsorship in form of money wins the election, as this gives the power to "un-create" the opposed candidate.