A simple search of Microsoft's site you have given you the
answer. Basically, FrontPage Extensions are a set of Microsoft server-side web CGI programs.
An example FrontPage extension is, when you create an image with various clickable areas (an imagemap), FrontPage will often set it up as a server-side imagemap using the FrontPage extensions to do the server processing. The catch is that the supposed "ease of use" of FrontPage Extensions really is just a way of trapping you into a Microsoft-only solution instead of a more open equivalent. So those imagemaps that FrontPage uses a proprietary extension for can be better handled as a simple W3C standard client-side image map that any browser can handle.
They are intended as ways for people who are too lazy or stupid to learn Perl, Active Server Pages, ColdFusion or PHP a way to add "cool" features to their site. Of course, if you use them and they don't work right or MS changes something in a release that breaks your site then you are SOL. Better to learn how to do it yourself. If you care, ColdFusion is the easiest to learn, ASP is the most prevalent, and PHP is the OpenSource option.