Short Answer
If one embraces the dichotomy between utterance and meaning, it becomes possible to claim that not all utterances, even if they look like propositions, have meaning, necessarily. A prime example of this is in the meta-ethical theory of emotivism put forth by A.J. Ayers and others that claimed that a statement like 'Killing is wrong' doesn't mean anything logically, but rather is an expression of emotion. This can be true if one takes it as fact that only truth-bearing utterances which obey a truth-conditional semantics have meaning. It is a radical view of truth and meaning; ultimately the logical positivists failed to defend this thesis in its extreme form. More broadly than ethics, the opposite of psychological emotivism is psychological cognitivism, which in the philosophy of mind tends to represent the mind as a symbol-manipulator. (See The “wisdom of repugnance” is said to be emotivism rather than intuitionism? Why is this? (PhilSE) for an example of how emotivism occurs in dialog.)
Long Answer
'Cognition' is used in two ways in philosophy and cognitive science. In the broad sense, it means all "products" of the mind, and in the narrow sense, it refers to those products which are considered rational, such as computation, logic, etc. So, in the narrow view of cognition, the primary preoccupation of the thinker is the rational aspects of the mind such as sense and reference, metaphysical necessitation, and logical reasoning. Today, it is almost universal that analytical philosophers use formal syntax to make philosophical arguments, and one might see the apex of that occurring in mathematics and science with the use of model theory and sophisticated logics such as intuitionistic logics and other abstractions. As such, analytical philosophers often see truth as existing independent of physical embodiment, and seek ways to ground their symbols in other symbols for meaning. In such a world, when one uses propositional logic it is easy to believe that the string "Killing is wrong" represented by P has no meaning at all because of the linguitic habit of divorcing syntax from semantics.
Remember, in philosophy generally, philosophers speak of sentences and propositions. When someone says "Killing is wrong", it is possible to begin breaking apart the proposition into parts and asking if other sentences are synonymous. Is P the same as the following?
- P2 Killing is always wrong.
- P3 Some types of killing are wrong.
- P4 Murder is wrong.
- P5 Preventing life is wrong.
- P6 Ending life is bad.
Some philosophers in the past have trivialized these sorts of cognitive questions claiming that it's "only semantics", but since the linguistic turn, analytic philosophers have worked very hard at producing a philosophy of language that explains language fully. Some philosophers of language, such as Richard Montague, have worked very diligently, in fact, to create abstract models of natural language, such as his Montague grammar, that seek to model all aspects of utterances. The problem often comes up, what to do with utterances that don't quite seem fully linguistic. "Ouch!" is an exclamation that isn't a proposition that strictly speaking has meaning (one could say "gazoizoig!" and the same effect would likely carry) since it doesn't demonstrate predication, but does signal to the hearer something. Logical positivists just take this line of thinking and extend it to utterances that appear to be propositions.
Lastly, in cognitive science, there are instances where language production is clearly pathological. These pathologies are collectively called aphasia, and in certain aphasias, it is possible to produce sentences that have meaning piecewise, but do not express complete thoughts, as in Broca's aphasia. Are such utterances expressing cognitive content? This is a philosophical question, and it is related to Chomsky's near-idiomatic expression 'Colorless green ideas sleep furiously'. What does it mean to have a clearly grammatical expression that seems to have meaning at the world level, but not so much as the level of proposition?
So, in philosophy of mind and the philosophy of artificial intelligence, it is defensible to recognize a dichotomy between psychological cognitivism and emotivism and ask questions about where does one draw the line. To be cognitivistic in one's thinking is merely to say that one is focusing on the symbols and their references as in the triangle of reference, an idea that goes back to Germany in the 19th century and reached mass consciousness with the formalisms of Gottlob Frege.