In 1940s, Claude Shannon developed the information theory focusing on quantifying the maximum data rate that can be supported by a communication channel. Guided by this fundamental work, the main theme of wireless system design up until the fifth generation (5G) was the data rate maximization. In Shannon's theory, the semantic aspect and meaning of messages were treated as largely irrelevant to communication. The classic theory started to reveal its limitations in the modern era of machine intelligence, consisting of the synergy between Internet-of-Things (IoT) and artificial intelligence (AI).By broadening the scope of the classic communication-theoretic framework, in this article we present a view of semantic communication (SemCom) and conveying meaning through the communication systems. We address three communication modalities: human-to-human (H2H), human-to-machine (H2M), and machine-to-machine (M2M) communications. The latter two represent the paradigm shift in communication and computing, and define the main theme of this article. H2M SemCom refers to semantic techniques for conveying meanings understandable not only by humans but also by machines so that they can have interaction and "dialogue". On the other hand, M2M SemCom refers to effectiveness techniques for efficiently connecting multiple machines such that they can effectively execute a specific computation task in a wireless network. The first part of this article focuses on introducing the SemCom principles including encoding, layered system architecture, and two design approaches: (1) layer-coupling design; and (2) end-to-end design using a neural network. The second part focuses on discussion of specific techniques for different application areas of H2M SemCom (including human and AI symbiosis, recommendation, human sensing and care, and virtual reality (VR)/augmented reality (AR)) and M2M SemCom (including distributed learning, split inference, distributed consensus, and machine-vision cameras). Finally, we discuss the approach for designing SemCom systems based on knowledge graphs. We believe that this comprehensive introduction will provide a useful guide into the emerging area of SemCom that is expected to play an important role in sixth generation (6G) featuring connected intelligence and integrated sensing, computing, communication, and control.