The first web server was hosted on a NeXT computer used by Tim Berners-Lee at CERN.
Berners-Lee developed the foundational World Wide Web software in 1990 while working at CERN, the European particle-physics laboratory. He used a NeXT workstation running the NeXTSTEP operating system because it provided powerful development tools and a graphical interface suited to rapid experimentation.
That machine ran the first web-server software, later known as CERN httpd, and hosted the first website at info.cern.ch. The site explained the World Wide Web project itself. The same NeXT computer was also used to create and run the original WorldWideWeb browser and editor.
A common mix-up is confusing the first web server with later servers outside CERN. The first server outside Europe went online at SLAC in California in 1991, where the software was adapted for an IBM mainframe. IBM therefore became important in early web hosting, but the original server ran on NeXT hardware.