Claude Shannon formalized the notion of information transmission rate and capacity for pre-existing channels. Wittgenstein in his later work insisted that linguistic meaning be defined in terms of use in language games. C. S. Peirce, the father of semiotics, realized the importance of sign, signified, and interpretant in processes of semiosis. In particular, the connection between sign and signified does not take place in a platonic vacuum but is situated, embodied, embedded, and must be mediated by an interpretant. We introduce a rigorous mathematical notion of meaning, as (1) agent- and observer- perceptible information in interaction games between an agent and its environment or between an agent and other agents, that is (2) useful for satisfying homeostatic and other drives, needs, goals or intentions. With this framework it is possible to address issues of sensor- and actuator- design, origins, evolution, and maintenance for biological and artificial systems. Moreover, correspondences between channels of meaning are exploited by biological entities in predicting the behavior or reading the intent of others, as in predator-prey and social interaction. Social learning, imitation, communication of experience also develop and can be developed on this substrate of shared meaning.