Can you just explain to me what the double dollar sign in front of rNee means?

It means dereference the reference.

Because genomic work often involves very large strings; and passing large strings into subroutines causes them to be copied:

sub something {
    my( $string ) = @_;
    ## $string is a copy of the argument 
}

my $hugeString = ........;

something( $hugeString );
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Instead of passing the arguments directly, I pass references (kind of pointers) to them:

fuzzyMatch( \$hay, \$nee, 3 ); ## pass references to needle and haysta
+ck
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Within fuzzyMatch(), it receives references to the two strings:

sub fuzzyMatch {
     my( $rHay, $rNee, $misses ) = @_; ## the 'r's are to remind that 
+these are references
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So to get to the actual strings, I use a second $

     my $lNee = length $$rNee; ## read as: $lenghtNeedle = length of t
+he data $, referenced by $rNee
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So, $$rNee is shorthand for ${ $rNee }; if that clarifies things for you?