The factors that differentiate language processing from linguistics and play a role in the field of cognitive psychology are language acquisition, language comprehension and language production. Since cognitive psychology is the investigation of all mental abilities, language processing plays a fundamental role in the field.
How a person acquires his language, for example, is telling not only of his mental faculties but that of those around him. In this case, the focus is on what kind of language is presented to a mind and what that mind selects to absorb and repeat. This allows scientists to study how one perceives one's environment and one's instructor, what one remembers, how one reasons, and how and to what extent one understands.
Language comprehension is the same, if not a step above acquisition. In studying reasoning, learning and perceiving, what one comprehends about not only one's language, but other languages presented to one is very telling. For example, if a subject only comprehends roughly one half of his own spoken language, hypotheses can be made about that subject’s comprehension of his written language. This demonstrates the subject’s mental abilities on several levels. How and under what circumstances a subject produces language also contributes greatly to cognitive psychology. It showcases what the subject remembers; i.e. what he had learned, how he perceives it, how well he understands it, and so on. It also shows how he reasons. What one person decides to say to another person speaks volumes about his cognitive abilities.
These precise separations between linguistics and language processing give the latter one of many important roles in cognitive psychology.