As a new function of 6G networks, edge intelligence refers to the ubiquitous deployment of machine learning and artificial intelligence (AI) algorithms at the network edge to empower many emerging applications ranging from sensing to auto-pilot. To support relevant use cases, including sensing, edge learning, and edge inference, all require transmission of high-dimensional data or AI models over the air. To overcome the bottleneck, we propose a novel framework of SEMantic DAta Sourcing (SEMDAS) for locating semantically matched data sources to efficiently enable edge-intelligence operations. The comprehensive framework comprises new architecture, protocol, semantic matching techniques, and design principles for task-oriented wireless techniques. As the key component of SEMDAS, we discuss a set of machine learning based semantic matching techniques targeting different edge-intelligence use cases. Moreover, for designing task-oriented wireless techniques, we discuss different tradeoffs in SEMDAS systems, propose the new concept of joint semantics-and-channel matching, and point to a number of research opportunities. The SEMDAS framework not only overcomes the said communication bottleneck but also addresses other networking issues including long-distance transmission, sparse connectivity, high-speed mobility, link disruptions, and security. In addition, experimental results using a real dataset are presented to demonstrate the performance gain of SEMDAS.