Halliday & Matthiessen (1999: 153-4, 155):
The particularistic model, then, comprises a set of submodels: (i) impacting, (ii) conscious processing, (iii) symbolic processing, (iv) relational ordering. The model that generalises across these various domains of experience is different from any one of these particular submodels. It sets up one central participant that is common to all processes. This is the participant through which the process comes to be actualised. We refer to it as the Medium: see Figure 4-9.
Semantically, the Medium is the participant through which the process is actualised. It is in the combination of Medium + Process that we find the complementarity we spoke of earlier between the temporal unfolding (the Process) and the atemporal persistence (the Medium).