This "sickness response" (which used to be called "sickness behavior") refers to "flu-like" symptoms that you normally would get with an acute infection, such as feeling feverish, unusual body aches, or alternating chills/sweating.
For me, this "sickness response" was an almost weekly event in the first few years of my ME, but it then faded. I haven't experienced any sickness response in over 10 years.
Michael vanElzakker often talks about the sickness response and its connection to the vagus nerve.