So... what would be an example of such an external program? Something that accesses a SQL database and changes values on the HTML page? I ask this specifically since you mention that database access would be prohibitively slow.
Or would you e.g. use CGI to call some script that changes the HTML? Let's say, post something that was written in an input box?
> So... what would be an example of such an external program?
The external program is responsible for producing the entirety of an HTTP response; headers and the message body (see here[0] for details). CGI allows a web server to provide what it knows from an HTTP request to an arbitrary program and expects it to write the response as it sees fit.
Think of it as a specialized case of "fork-exec"[1] where the "child process" has the responsibility of writing the raw HTTP content to the "parent process" (the web server).
In the CGI model, each request causes a "fork-exec"[1] and, as such, any interaction with other services (such as a database) requires connecting, using it, then disconnecting each time. This can quickly swamp server resources, which lead to the definition of FastCGI[2] to help alleviate this type of thrashing.
HTH
0 - https://tools.ietf.org/html/rfc2616#section-4
BTW, is this kind of specialised fork-exec code that writes back HTML code to the parent process still in use?
Yes, but is most likely found in intranet situations. As others have noted, commercial offerings typically use an application server style approach, as that greatly contributes to being able to scale.
However, not everything has to scale ;-).