So let's see what this does:

$z= $0; # store the name of the script in $z
$z=~ s{.*    # anything, greedy match
         /   # then a / (the last one in $z as the match is greedy)
       }{}x; # removed
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So this snippet just returns the basename of the script.

And as you see you can also use brackets like { } as delimiters, and the x modifier lets you comment the regexp.