Generally, the term psychology refers to the study of the mind – William James defined it as ‘the science of mental life, both of the phenomena and their conditions’ in his ‘Principles of Psychology’. The definition has changed somewhat since James’s time, but broadly that seems to be a good working definition.
What would a more theologically informed definition of psychology be, however? I’m hardly an expert on physiology, but here is what I would suggest: a theological psychology is holistic and unified – rather than treating the mind as totally separate from the body it would act on the knowledge of man as a unity of body and spirit. This would therefore be a broader kind of study – not limited to only studying mental workings (which are separate from and cannot be reduced to brain activity, but obviously are dependent on the body). A theological psychology would be a discipline that would study the whole of man, because man is a unity – but though man is a unity that does not mean that there are not differing aspects to this unity that must be studied/treated differently.
There remains much to be worked out here, and I can only reiterate that I am far from an expert on psychology. I expect a fair amount of criticism and refining to take place here.