Others have already pointed you at parts of the Perl documentation you need to read. Though your test code doesn't compile even without strict and warnings, please note for future reference that you should always turn on strict and warnings, especially if you're unsure of the syntax. In your example test code, doing that produces an extra warning, namely:

Scalar value @msgs[0] better written as $msgs[0] at f1.pl line 5.
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This is such a common Perl syntactic oversight that use warnings helpfully warns you of it. For more information on this particular common coding mistake, please see Common problems with slices from the excellent series of Perl tips provided by Perl Training Australia.

If I understand you correctly, you want something like:

use strict;
use warnings;
use Data::Dumper;
my @msgs;
push @msgs, [ "1st array: line 1", "1st array: line 2" ];
push @msgs, [ "2nd array: line 1", "2nd array: line 2", "2nd array: li
+ne 3" ];
print Dumper(\@msgs);
my $i = 0;
for my $arr (@msgs) {
   ++$i;
   print "array $i:\n";
   for my $line (@{$arr}) {
      print "  $line\n";
   }
}
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