A recursive sub is when a sub calls itself in some form.
The best example of this usually given is the mathematical function factorial (denoted by !). Are you familiar with it? 4! = 4*3*2*1. 7! = 7*6*5*4*3*2*1. In general, n! = n*(n-1)*(n-2)*...*2*1. But you could also say that n! = n*(n-1)!.

so if you would make a sub called factorial, then it would be something like this:

sub factorial {
     my $n = shift;
     return $n * &factorial( $n - 1 );
}
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but this obviously doesn't work, 'cause it will keep going and going, so you need a stopping point too.

sub factorial {
     my $n = shift;
     if ( $n == 1 ) { return 1 }
     return $n * &factorial( $n - 1 );
}
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Try searching Google for recursive functions, recursive subs, recursion, etc.