As autonomous systems and embodied intelligence enter the dynamic physical world, multi-agent collaboration calls for a paradigm shift in communication design. However, existing communication paradigms overlook that agents form action understanding from their own states, environmental observations, and collaboration relations through a process that evolves as a task unfolds. Consequently, reliable bit delivery, general semantic recovery, or single-task utility optimization alone cannot ensure that heterogeneous agents form coordinated actions compatible with their own conditions from shared information during task execution. To address this gap, this paper proposes embodied semantic communication (ESC) as a paradigm that transforms information transmission into action-oriented semantic interaction. Specifically, ESC characterizes how an explicit communication link can encapsulate multimodal perceptual states, intrinsic hardware capabilities, and collaborative intents into unified actionable semantic representations, thereby enabling heterogeneous receiving agents to parse, align, and ground them in local motor control. This paper clarifies the conceptual boundary, system characteristics, and environment-constrained technical pathways of ESC. It maps the underlying mathematical tools, including semantic information theory, world models, and multi-agent decision theory. Finally, this paper summarizes key open challenges, including measurable semantic reliability, ambiguity-triggered interaction under dynamic environments and tasks, and bandwidth-adaptive semantic transmission, outlining a roadmap for collective embodied networks.

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