What Web Servers Do

Return files located by Universal Resource Locators (URL's) using the Hypertext Transport Protocol (HTTP).: These files documents are usually formatted using the Hypertext Markup Language (HTML).
Decide who can have files and who cannot (security).: Also in the topic of security is a draft specification for secure HTTP, and information from NCSA on using encryption in the HTTP protocol.
Use the MIME standard for file types to determine how to transfer files. Here is the MIME specification.
Execute programs and scripts using the CGI protocol.: CGI is generally accessed through forms, which can be used for email or gateways such as with WAIS, for example.
Provide support for image mapping. Here is an imagemap tutorial from Caltech, and another: imagemap tutorial from NCSA.
Act as a proxy for clients behind a firewall. Here's another firewall FAQ.
The CERN server is capable is of caching when used as a proxy.