The main job of a web server - any web server, is to find the document that the user has requested (usually by clicking on a link) and send it back to them. The kind of web server and its' capabilities have a big impact on the web site.
FrontPage not only creates the HTML for the web page, but it has a number of prebuilt scripts (programs) that can be inserted for other functions in the page. Without FrontPage, you'd have to get these scripts from your ISP or other sources, and many ISP's are particular about the scripts that they allow to run on their servers for performance and security reasons.

Consider the hit counter, it is a good example of what I'm talking about.
When you ask for a page that has a hit counter on it, the web server locates that page and runs the hit counter program. The hit counter program takes the number of times the pages has been requested adds 1 to it and gives that number to the web server. The web server adds that number to the web page where the hit counter wants it to display. Now what the FP Server Extensions do (in this scenario) is to enable communication between the web server and the hit counter program. Without the Server Extensions, the hit counter program would never be triggered. Without the Web Server the count would not be placed on the web page and delivered back to the browser.
Now, do you need the PWS (Personal Web Server) on your local computer? Only you can answer that, but most people like to test their site before uploading it to their ISP. However, it is certainly not a requirement.

For the relevant Knowledge Base articles - check out
<A target="_blank" HREF=>FP2000: Features That Require FrontPage 2000 Server Extensions(Q232524)</A>. (If it requires server extensions, it would also require a server.)
<A target="_blank" HREF=;EN-US;q281532>FP2002: Features That Require the FrontPage 2002 Server Extensions(Q281532)</A>

Dynamic html components (DHTML) do not require either a web server or server extensions, because DHTML is rendered by the browser, not a web server.