The "great packing machine" refers to the slaughter industry the author describes through the book. He is trying to portrait and denounce the unhealthy, dangerous, almost-enslavement condition the workers suffer in that industry.
The phrase "the great packing machine" refers to the slaughter industry. This is the industry that the author discusses in his book "The Jungle." In this book, the author shows the shortcomings of the meat packing industry in the United States. We learn that this industry was extremely unsanitary, a fact that shocked readers. We also learn that the workers who work in this industry often faced long and difficult hours, harsh work and very low pay.
