Actually, this does have to do with continuations, or at least the notion of CPS (continuation-passing-style). The basic idea of CPS is to turn all non-tail recursive calls to tail calls (which is equivalent to iteration) by explicitly managing your stack. This is done by adding an additional parameter that represents the explicit continuation. The end result is that your heap allocation grows larger, but at least you won't blow up the call stack due to all those non-tail recursive calls _if_ the language you're working in 'properly' handles tail calls.
For example, a version of factorial that becomes deeply recursive:

sub fact {
    my $num = shift;
    return 1 unless ($num);
    return $num * fact($num - 1);
}

sub tail_fact {
    my ($num, $k) = @_;
    return $k->(1) unless ($num);
    return tail_fact($num - 1, sub { return $num * $k->(shift); });
}
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Here we're manually representing the rest of the computation (the continuation) as an anonymous sub that keeps growing and growing... of course, the other alternative is to just represent the actual number we've accumulated thus far, but then that'd just be accumulator-passing-style.
Of course, none of this really matters since Perl doesn't handle tail calls properly. It'll still warn you that a "Deep recursion on xxx" unless you change it to a strictly iterative version using while or for or one of those guys.