Halliday & Matthiessen (1999: 513-4):
At the same time, while recognising a general category of "process" to construe our experience of change, the grammar also recognises that not all processes are alike. As human beings we become aware (and again we can see this in the actions of tiny infants) that phenomena fall into two distinct types: those happening outside ourselves, which we can see and hear, and those happening within our own consciousness — thoughts and feelings, and also the sensations of seeing and hearing, as distinct from whatever is seen and heard. The grammar construes this as a distinction between "material processes" and "mental processes". Mental processes are specifically attributed to conscious beings: humans, and some of our more intimate animal consorts.
Languages construe this pattern in many different ways, and draw the line at different points; as always we are relating our account to the particulars of English. Here the grammar postulates a third type of process intermediate between these two: "behavioural" processes, in which inner events are externalised as bodily behaviour, like staring, thinking (in the sense of pondering) or crying.