Overly wordy placeholder for Holly, who will flesh this out herself asap:
Three of the big names in cognitive psychology are associated with the theory that cognition is embodied, or based in physical experience. Eleanor Rosch (Thing #35) and collaborators published a book titled The Embodied Mind (1991). They wrote, "By using the term embodied we mean to highlight two points: first that cognition depends upon the kinds of experience that come from having a body with various sensorimotor capacities, and second, that these individual sensorimotor capacities are themselves embedded in a more encompassing biological, psychological and cultural context."
George Lakoff has written extensively on the topic, arguing that all cognition is grounded in bodily experience and action. Most influential, his research on people's understanding and use of metaphors reveals that people use physical knowledge to understand abstract concepts (e.g., think for a moment of your knowledge about what concepts are, and you'll realize that our knowledge about concepts and categories is anchored in our physical experience with containers and territories, with some things in the category and other things near the boundary and so forth). I strongly recommend his books The Metaphors We Live By (1980) and Women, Fire and Dangerous Things (1987).
Perhaps the best-known advocate of the embodied-cognition view is Larry Barsalou, who prefers the broader term "grounded cognition" to convey that knowledge is grounded in physical experience rather than being amodal and purely symbolic. For an overview, see http://matt.colorado.edu/teaching/highcog/readings/b8.pdf