The word "cognition" refers to the contents of the mind by which we know or understand the world about us. But the contents of the mind are not all cognitive.
Examples of noncognitive mental contents are our bodily feelings, our pains and aches, as well as our emotions and sentiments. We are directly aware of such noncognitive mental content, a toothache is not id quo, but id quod -- something that we directly apprehend rather than that by which we hold some object before our minds.
This definition raises a question about whether we can converse with others about our pains and aches. The dentist I talk to about my toothache has no experience of it. It is mine alone. I can describe it to him and he can understand my word, but he cannot feel it.
If communication involves having a shared object to discuss, then is my conversation with my dentist about my toothache communicative? Strictly speaking, the answer is no. But if my dentist ever had a toothache himself, he can imagine what a toothache is like while I am talking about the toothache I am having. To that extent, we can be communicating even if the toothache is not the same object for both of us.