It just means that given $array_ref = [qw/bar baz/]

$$array_ref[0] is the same as $array_ref->[0]

Similarly, given $hash_ref = { bar => 'baz' }

$$hash_ref{bar} is the same as $hash_ref->{bar}

I've traditionally preferred the double-sigil style, mostly because I strongly disliked the arrow syntax when I first started coding Perl. I think though it is generally regarded as bad because it isn't quite so explicit, and I admit my own opinion on the matter is gradually shifting toward the arrow.

Another example:

%hash{array_ref} = [];
push @{$hash{array_ref}}, 'thingy';
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Here the reference is a value in a hash that points to an array which must be dereferenced before being passed to push