Apache is the WebServer for Linux. It also runs on most other OpenSource (and not so open source) OperatingSystems. It started life as a heap of patches circulating for NCSA's httpd which was no longer maintained. Eventually, a group of developers collected all the patches and consolidated them into their own version of the web server - "A Patchy Server". Hence the name, "Apache Server".
Apache is one of the critical components of LAMP (Linux/Apache/MySQL/PHP).
The Apache OpenSourceProject has many subprojects (which they confusingly call projects, but never mind), including: the Apache HTTP Server, the Ant build program, the XML project (which releases Xerces, Xalan and AXIS) and the PHP ProgrammingLanguage.
See Also:
39 pages link to Apache:
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