While you should read the above mentioned docs, here is a very simple explanation.
Somewhere before this line, $RESPONSE is being set to point to another variable. Something like:

$x = 3;
$RESPONSE=\$x;
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After this, $RESPONSE contains the memory address of the $x variable.
If you print $RESPONSE you will get a strange string. Something like "SCALAR(0xec94c)". Which says that $RESPONSE is a reference to a scalar (at memory address 0xec94c).
To get to the value that $RESPONSE is pointing to you need to dereference it. Putting the extra $ before the variable, is a way of dereferencing the variable (there are others, see the docs). Thus if you print $$RESPONSE, you will get 3.
You can also assign to the dereferenced variable. Doing so would change the value stored in $x.
In your case, whatever $RESPONSE is pointing to will have its value changed to 0
Hope that helps,