Here is the foreword to the article in Wikipedia:
The Polyvagal theory (gr. ‘polus’, “‘many’” + ‘vagal’, “‘vagus nerve'”) specifies two functionally distinct branches of the vagus, or tenth cranial nerve. It serves to identify the relationship between visceral experiences and the vagus nerve’s parasympathetic control of the heart, lungs, and digestive tract. The theory was introduced in 1994 by Dr. Stephen Porges, director of the Brain-Body Center at the University of Illinois at Chicago. According to the theory and its increasing evidence base, the autonomic nervous system is interconnected with and sensitive to influences that flow from the body toward the brain, called afferent influences. This effect has been observed and demonstrated by adaptive reactivity dependent on the neural circuits’ phylogenetical development. It builds on the study of what Charles Darwin referred to as the “pneumogastric nerve.” The polyvagal theory claims that humans have physical reactions, such as cardiac and digestive changes, associated with their facial expressions. Porges argues this theory with observations from both evolutionary biology and neurology.
The branches of the vagal nerve serve different evolutionary stress responses in mammals: the more primitive branch elicits immobilization behaviors (e.g., feigning death), whereas the more evolved branch is linked to social communication and self-soothing behaviors. These functions follow a phylogenetic hierarchy, where the most primitive systems are activated only when the more evolved functions fail. These neural pathways regulate autonomic state and the expression of emotional and social behaviour. Thus, according to this theory, physiological state dictates the range of behaviour and psychological experience. Polyvagal theory has many implications for the study of stress, emotion, and social behaviour, which has traditionally utilized more peripheral indices of arousal, such as heart rate and cortisol level. The measurement of vagal tone in humans has become a novel index of stress vulnerability and reactivity in many studies of populations with affective disorders.
In order to understand the deapth of the theory, here is a basic paper: The polyvagal theory: phylogenetic substrates of asocial nervous system by Stephen W. Porges.