TL;DR The “original” Illuminati were a bunch of scientists trying to advance research in medicine and astronomy whilst avoiding prosecution by the (deeply catholic) bavarian authorities. Our understanding of a “secret world domination” order has nothing to do with what the Illuminati were!
Originally, “the Illuminati” refers to the “bavarian Illuminati” founded some time in the 1770s in a little town called Ingolstadt (thats where Audi, the car brand, comes from). It was a group founded to secretly pass on scientific knowledge and advance research especially regarding medicine and astronomy. The reason why they had to turn it into a secret order was the deeply religious and conservative society back then, which basically deemed science the work of the devil.
About 15 years later they were officially disbanded and the bavarian king banned them along with the freemasons and other secret orders. Later on it was claimed that they never ceased to exist and that their influence has led to various historical events such as the french revolution, the two world wars or the terrorist attacks on 9-11.
There is no evidence that this order still exists (compared to the freemasons, who are still very active) and it definitely never was anything like the secret world domination order we think it was… That’s mostly due to shitty books like Dan Browns Illuminati and some ridiculous US historian (cant remember his name, sorry) who basically made up their stories and spread them out across the world…
If you want to know more I can post some more information later on…
Source: I am from that area and have worked as an intern with historians researching the secret orders from back then and their influence nowadays.