When most people refer to Apache they are talking about the "Apache HTTP Server Project". In fact Apache is really the "Apache Software Foundation" which hosts a long list of projects of which the HTTP server is just one, albeit the best known.
The Apache HTTP Server enables web pages to be published on the internet (or an intranet or even on a single test machine). The PHP scripting language, in which Moodle is developed, is tightly integrated with the Apache HTTP Server. A web server is a required component of a Moodle installation. There are two distinct developments of the Apache HTTP Server, version 1 and version 2. Although version 2 should have replaced version 1, the architectures are so different that they both continue to be supported. Either are fully supported by PHP and Moodle.
The Apache HTTP Server Project describes itself thus:
"The Apache HTTP Server Project is an effort to develop and maintain an open-source HTTP server for modern operating systems including UNIX and Windows NT. The goal of this project is to provide a secure, efficient and extensible server that provides HTTP services in sync with the current HTTP standards.
Apache has been the most popular web server on the Internet since April 1996. The November 2005 Netcraft Web Server Survey found that more than 70% of the web sites on the Internet are using Apache, thus making it more widely used than all other web servers combined."