FastCGI and mod_perl are two approaches to solve one problem of Perl CGI scripts -- namely, that the web server has to start the script from scratch each time it is called. That means the OS has to locate and load the file, start the interpreter, let the interpreter parse, compile, and finally execute your script every time someone accesses it.

FastCGI and mod_perl do everything but executing the script, and they keep it around, compiled, to avoid all of the startup each time someone wants to access it. That can be a big performance gain.