Just take a deep breath and walk through it piece by piece. It will become clear if you leave the keyboard for a few minutes and return with a fresh head.

my @arr = qw(book dog cat);
print  "['"               # Print the leading bracket and quote
     . join("','", @arr)  # join array with quotes and commas
     . "'];\n";           # print the trailing quote, bracket, etc.
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Extra whitespace added for clarity.