with #!/your/path/to/perl you force the use of a specific version of perl to be executed.

The line #-*- perl -*- is for someone using emacs, and can be dropped. It should force emacs to use perl syntax highlighting, even if the command itself is a shell.

The exec perl -x $0 "$@" line in the sh script executes the first perl executable found in $PATH, and would be somewhat equivalent to a header like #!env perl, which won't run on some systems. In both cases you have the risk of using modules that are not installed in either. Personally I always use the #!/my/personal/perl version.