Systems such as Catalyst or Mojolicious are frameworks that provide more of the infrastructure that are needed by ... well ... “the sort of web-sites that Catalyst or Mojolicious are good at building.” Each of them has ecked out a particular piece of common-ground and made it very easy to build websites along the same lines.
They also are typically designed so that they can be used under mod_perl, FastCGI, Plack, or CGI mode.
The essential purpose of these “non-CGI” arrangements is that the software is, by whatever means, no longer repeatedly loaded and unloaded with each request, but remains persistent ... either as a Perl interpreter wedged into apache, or as a cadre of service-processes who fulfill requests handed to them by Apache.