In addition to the things IlyaM mentions, I'd add,

6. FastCGI processes can run on a separate computer from the web server.

All FastCGI does it take an HTTP request and send it, with appropriate delimiters, to another socket and then wait for a response. What makes it fast is that you can then structure your program like this:

Initialization ...
while (new CGI::Fast) {
  main CGI loop
}
[download]

You can thus service many requests without the all the overhead of process start-up, Perl compilation, DB opens, etc. Except for separating the initialization code, FastCGI usually doesn't require any changes to your program. You often do have to make some more changes for mod_perl, although usually not much.