This assumption is not made arbitrarily of course, and I believe that there is a preponderance of evidence in favor of this conclusion. First, obviously, when the structural integrity of the brain is compromised, the functions of the mind can suffer (as in certain cases of aphasia) or cease working altogether. More evidence is seen by the fact that we can and do often alter the state of the mind through antidepressants, antipsychotic drugs, and even psychedelic drugs, in essence changing the state of the mind by changing the chemical composition of the brain. These things all seem to suggest that the mind is indeed as much a part of the physical world as everything else. We can only assume then that our state of mind can be instantiated in a physical form, that our consciousness is determined by a specific chemical state and /or set of electrical discharges within the brain. This state is material in nature and thus follows the same causal laws that all matter must observe.
The physical world is governed by causal laws. This is the most important assumption in the thesis of determinism. The consequence of this assumption is that our state of mind, ultimately determined by a physical form, must follow some sort of causal laws. This assumption does not mean that the chemical or material composition of the mind is not affected by the outside world, indeed quite the contrary. Our mind and therefor our brain chemistry is constantly affected by the outside world through our senses, but this interaction with the outside world is determined by our current state of mind and the state of the world at any particular instant. Therefor, this causal change in one's state of mind can be seen as determined once all causes internal and external have been accounted for. .
I believe it is becoming clear at this point what is meant by Determinism. Yet at this point the physicist might object that we can't determine the path of matter or energy accurately, and can only at best have statistical laws with which we can determine the motion of matter.