Embodiment is currently a hot topic in psychology and philosophy, for good reasons. Thinking is heavily influenced by physiological processes involved in perception and emotion. Embodiment is a useful extension to cognitive theories that explain thinking in terms of mental representations, but not an alternative theory.
Since the 1960s, the dominant approach to cognitive psychology has been to explain different kinds of thinking in terms of computational procedures that operate on mental representations. Such representations include not only verbal ones such as word-like concepts and sentence-like propositions, but also visual images and neural networks. In the past decade, an increasing number of researchers in both psychology and philosophy have argued that the standard approach has neglected the important role that human bodies play in cognition. Our concepts are not like the verbal and mathematical structures that are easy to represent in current computer languages, but rather combine many kinds of perceptual information that depend on the sensory systems that operate in our bodies. Psychologists such as Larwrence Barsalou have provided experimental evidence that concepts are parts of perceptual symbol systems. For example, your concept of a car is far more than a verbal description of typical cars, since it can also include sensory information about how cars look, sound, smell, and feel.
Research on emotion also provides evidence for embodiment. Thinking is inseparable from emotion, and emotion involves physiological changes in heartbeat, breathing, skin response, hormone levels, and so on. Rather than a distraction from effective cognition, emotion is crucial to it for providing estimations of value and motivations to act. Emotions are not just abstract judgments about the relevance of situations to our goals, but also require the brain's reaction to bodily changes.
It is important, however, not to exaggerate the importance of embodiment and throw out the many insights that the computational-representational approach to thinking has afforded. Cockroaches are embodied too, but they're not very smart. We need to distinguish the moderate embodiment thesis that language and thought are shaped by embodied action from the extreme embodiment thesis that thinking is just embodied action that does not require representation and computation. The extreme view has been advocated by Heideggerian philosophers and by a few psychologists who claim that the brain is a dynamic system but not a computational one. The brain is undeniably a dynamic system, but so are galaxies and ecologies that lack the capacity to think. Explaining how people can solve problems, make inferences, and use language requires appreciation of highly sophisticated computational procedures for manipulating representations. Hence the accumulating evidence for the role of the body in perception and emotion supports the moderate embodiment thesis, not the extreme one.
In another post, I advocated a view of emotion that combines cognitive appraisal and physiological perception. Emotion is far too subtle to be just a reaction to bodily changes. There are hundreds of different emotion words in English, and emotions cannot be differentiated by physiology alone. Cognitive appraisal is required for differences among basic emotions such as fear and anger, and especially for differences among social emotions such as pride, arrogance, embarrassment, shame, and guilt. Hence embodiment should be viewed as an important aspect of human thinking, not as the whole story.