Image via WikipediaOn Aug. 6, 1991, Tim Berners-Lee first shared his ideas for the World Wide Web via the Internet. (Yes, the Internet and the World Wide Web are different things, though the distinction is more nebulous these days.) Berners-Lee actually waited several months before sharing his Web concepts with the larger online world; history's first Web server went live from CERN on Christmas Day 1990.
In the interim, Berners-Lee spent time perfecting his World Wide Web software, including the concepts of a server and a browser. He did all this on a then-outdated workstation running an operating system that was neither Windows, Macintosh, nor Linux (the last of which wasn't even invented yet).
What operating system ran the world's first Web server?
The world's first Web server, CERN httpd, was developed with and ran upon a NeXT computer running the NeXTSTEP operating system, which itself was derived from Unix.
For those that don't know, NeXT was the computer company that Steve Jobs founded after he was fired from Apple. The NeXT computer that Tim Berners-Lee used to write the world's first web server software was a classic Jobs product: A one-foot-square aluminum cube that cost $6500 when it was released in 1988. The NeXTSTEP OS was a Unix variant with a graphic user interface, which is pretty much the same description you'll find for Mac OS X today.
Unlike the modern Mac (but very much like the first one), the NeXT Computer was already discontinued when Berners-Lee used it to run his first Web server. That server software was, not surprisingly, almost immediately ported to other still-in-production Unix-based operating systems. Today, the original CERN httpd box is part of the science history museum at CERN itself, guaranteeing the failed NeXTSTEP OS at least one more footnote in computing history and the archives of the Truly Trivial.