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, the main theme of wireless system design up until 5G was the data rate maximization. In his 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 IoT and AI. By broadening the scope of the classic 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, the main theme of the article, represent the paradigm shift in communication and computing. H2M SemCom refers to semantic techniques for conveying meanings understandable by both humans and machines so that they can interact. M2M SemCom refers to effectiveness techniques for efficiently connecting machines such that they can effectively execute a specific computation task in a wireless network. The first part of the article introduces SemCom principles including encoding, system architecture, and layer-coupling and end-to-end design approaches. The second part focuses on specific techniques for application areas of H2M (human and AI symbiosis, recommendation, etc.) and M2M SemCom (distributed learning, split inference, etc.) Finally, we discuss the knowledge graphs approach for designing SemCom systems. 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 6G featuring connected intelligence and integrated sensing, computing, communication, and control.