It's effectively a "cast to boolean" operation.

Consider you have a variable $x which might contain a string, or might contain a number - you're not quite sure. If you want to force it to be treated as a string, you do something like this:

    say ($x . "");  # concatenate an empty string to it
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Or if you want to force it to be treated as a number:

    say ($x + 0);   # add zero to it
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!! does the same for forcing things to be a "boolean". Perl doesn't have real booleans (though there are CPAN modules for that) so in this case uses the empty string to represent false, and the number 1 to represent true.

How does it work? A single ! is just a "not" operation. Two not operations cancel each other out truth-wise, but still act to cast the value to boolean.