Bodymind is a concept for understanding body and mind as a single holistic unit.
You already know how mind and body influence each other. When your stomach is empty, it signals to your brain (via ghrelin secretion) that it needs food. Suddenly you’re thinking about pizza—your body influenced your mind. Then you consider how beef is actually much better and you start cooking, eating, and digesting a delicious steak—your mind influenced your body.
You also know the story about posture, right? 
Harbor negative thoughts, and it will show in your posture—because your mind impacts your body. Conversely, you can adopt a power posture to increase your confidence and make positive thoughts emerge—because your body impacts your mind. Try to fill in the “…” in the two pictures. Easy, indeed.
Two everyday examples should be enough. You can easily come up with more on your own. Think about love, sports, or placebo effects. Still, you’ll probably have reservations about the implications: Mind and body are interrelated, ok, but this doesn’t mean that they’re the same! Or does it?
Pragmatic Approach
First of all, keep in mind that language is inherently pragmatic. I can use words however I want—and fuak you if you disagree! As long as the recipient of my babbling gets the intended meaning, my use of words was correct. I can call an apple an orange, and it’s not wrong as long as I ensure that the person I’m talking to has a chance to grasp what I intend to say.
Ultimately, all is one—philosophically speaking. Linguistic categories (words) are artifacts that more or less arbitrarily divide our human experience of this all-encompassing oneness. The objective is successful communication. Therefore, “mind equals body” is a true statement if it makes pragmatic sense to use this equation in a given conversation, while “mind doesn’t equal body but is only bidirectionally connected to it” may be just as correct if the conversational context is different.
This probably doesn’t sound very scientific to you. Let me continue…
Scientific Approach
In modern cognitive science, the hype about embodiment has still not worn off. Embodiment means that cognitive processes & systems are deeply rooted in the body’s current, past, ontogenetic, and even phylogenetic (evolutionary) sensorimotor interactions with the world. Cognition doesn’t just have an underlying physiological structure in the nervous system, it’s also fundamentally inseparable from the body, its physical characteristics, and how it behaves in the environment.
One example of embodied cognition is the action-sentence compatibility effect (investigated by Glenberg & Kaschak). 
Let’s say you have a control device in front of you (like the upper one in the picture) with two buttons: Y for “yes” is located a bit further away from you than N for “no” (your finger rests in the middle). If you now have to judge whether the sentence “She opened the drawer” makes sense, it will take you longer to click on Y than if you had to judge the sentence “She closed the drawer.” By contrast, let’s now assume that you have another control device in front of you (like the lower one in the picture), where Y is closer to you than N. Now it will take you longer to press the yes-button for the sentence that describes an action in which you typically move your hand away from the body (closing a drawer). How is this possible? There seems to be a statistical interaction between implied sentence direction (open vs. close drawer) and actual response direction (move button-pressing finger closer to vs. further away from body). This indicates that language understanding taps into action-based systems, which supports the hypothesis that linguistic meaning is grounded in bodily activity and the brain’s motor cortex.
Similarly, it has been shown (by Hauk et al.) that the comprehension of action words (e.g., “lick”, “kick”, “pick”), which are semantically related to different parts of the body (e.g., tongue, foot, hand), activates the motor system in a somatotopic manner. This means that thinking about licking activates that part of your brain that’s responsible for motor actions of your tongue. Mind and body are intrinsically related.
Mirror neurons are another prime example of how cognition is embodied. Mirror neurons are cortical motor neurons that discharge both when executing and when merely observing (or even just thinking about) an action. They enable us to understand other people’s gestures, postures, goal-directed motor acts, and emotions. Without the motor areas in our brain we wouldn’t only lack our ability to do stuff, but also our ability to comprehend what others are doing. Mind and body are, in this sense, inseparable. By the way, the mirror neuron system even enables us to gain physical strength through thinking alone.
Psychosomatic medicine is another assumedly relevant discipline. Research in this field has shown over and again the many ways in which psychosocial stress (the opposite of mindcoolness) affects hormonal and cellular processes. For example, rumination and worry produce adverse physiological effects. Introduction to Psychoneuroimmunology
I don’t want to provide a comprehensive, detailed scientific analysis of bodymind theories here. This whole article is intended as a painting to fill your bodymind with various impressions about the bodymind. (Do you see the terminological difference here? Despite the possibility, it’s not useful to regard all mental functions as bodymind functions.)
Therapeutic Approach
In somatic psychology, which provides the basis for body psychotherapy
A straightforward example of the bodymind in body psychotherapy is Alexander Lowen’s bioenergetic analysis, which attempts to “understand the human personality in terms of the human body” (Bioenergetics
Sure, linear and direct links generally oversimplify things, and sure, the psychotherapeutic approach relies heavily on clinical knowledge, which is not (yet) sufficiently supported by scientific knowledge. Nonetheless, in order to assimilate the bodymind concept I find it worthwhile to reflect on this approach’s fundamental principle that you are your body.
Philosophical Approach
Philosophically, if you need to give it a title, the bodymind is best understood in terms of dual-aspect monism. Monism claims that reality consists of only one fundamental substance (not two as in mind-body dualism) that is neither mental nor material. Rather, mental and physical entities are irreducible descriptions of, or perspectives on, this one reality—that’s the dual aspect of it.
I won’t discuss deep metaphysics here though, for it really has no practical relevance to anything. In the end, it always boils down to what kind of language game you want to play (consider again my linguistic approach above). I suggest you rather go outside and play for real.
Spiritual Approach
In case you’re a rebel and didn’t comply with my suggestion to go outside, consider finally my spiritual approach to the bodymind. Any random hippie or New Age enthusiast will be able to blather about it for hours. There’s no value in that. Likewise, I find it boring to recite the ancient wisdom of Buddhist, Taoist, Hinduist, Sufist, Yogist, Whateverist traditions.
Let’s keep it simple.
Your bodymind is your inner body that you can access and be via breathing and feeling.
Aaaaand that’s the perfect point to shut the fuck up.