I haven't read anything precisely on the intelligibility of science explanations.

However, I know science communication is an active research area concerned with how science efficiently and effectively amongst academics and to the general public. This might be a fruitful keyword to Google. 

I have also read a few articles on the theory communication in general which may offer some useful insights into the intelligibility in scientific explanations. I would recommend the book "Philosophy of Communication"  (link bellow), which includes many seminal works on this subject by Wittgenstein, Derrida, Leibniz, Plato and others. These are worth reading in and of themselves.

The paper "A mathematical theory of communication" by Shannon is  a must read. It has massively influenced the way I think about the communication of my work.  

I hope this helps, I am sorry I couldn't offer a more specific answer on the communication of neuroscience and psychology.

http://mitpress.mit.edu/books/philosophy-communication-0

http://dl.acm.org/citation.cfm?id=584093

I haven't read anything precisely on the intelligibility of science explanations.

However, I know science communication is an active research area concerned with how science efficiently and effectively amongst academics and to the general public. This might be a fruitful keyword to Google. 

I have also read a few articles on the theory communication in general which may offer some useful insights into the intelligibility in scientific explanations. I would recommend the book "Philosophy of Communication"  (link bellow), which includes many seminal works on this subject by Wittgenstein, Derrida, Leibniz, Plato and others. These are worth reading in and of themselves.

The paper "A mathematical theory of communication" by Shannon is  a must read. It has massively influenced the way I think about the communication of my work.  

I hope this helps, I am sorry I couldn't offer a more specific answer on the communication of neuroscience and psychology.

http://mitpress.mit.edu/books/philosophy-communication-0

http://dl.acm.org/citation.cfm?id=584093

I guess David Marr's Three Levels of Analysis (sometimes called the tri-level hypothesis) is, in a way, a theory about how we communicate and collate research done by different disciplines concerned with the study of the mind.   

You migth want to take a look at "Intelligibility is Necessary for Scientific Explanation, but Accuracy May Not Be" or at Mieke Boons contribution to Scientific Understanding: Philosophical Perspectives (Henk de Regt ed.)

http://mindmodeling.org/cogsci2012/papers/0244/paper0244.pdf

Jan Arreman:

It seems to be an excellent book, I can read a little on GoogleBooks, but I don't have the full version, sadly. Thank you very much for the article!

Renzo Bianchi:

I think in something like this

"Intelligibility (or understanding, if you prefer) is brought about when one sees how the phenomenon is produced according to a familiar, acceptable set of more basic beliefs, or how a mechanism, and entities and activities that comprise them, produces the phenomenon of interest in accord with some more basic beliefs."

(...)

"Intelligibility depends crucially on comprehending the continuity among the entities and activities that comprise the mechanism that is the explanation. This continuity is not the unifying of domains spoken of by Michael Friedman and Philip Kitcher. It is the continuity or sense that is inherent in the already accepted relations among entities and their activities that make for a coherent narrative. This why they may be used as part of a mechanism to explain a stage in the process about how a mechanism produces a phenomenon."

Machamer (2009 manuscript), Explaining Mechanisms, p. 6

Maybe this paper could be of your interest:

https://www.researchgate.net/publication/262022724_When_do_models_provide_genuine_understanding_and_why_does_it_matter

Article When do Models Provide Genuine Understanding, and Why does it Matter?

Adrian, causal theories are considered fundamental for explanations in science generally, and provide the basic assumptions concerning accepted relations among entities and their activities. What can comprise a coherent narrative likewise depends on assumptions about causation. Some think narratives are only considered to be coherent if they rely on some theory of linear causation, these are your positivist empirical explanations. Others are interested in dialectical or emergent causation. To be intelligible, you should identify which assumptions you accept, and how your explanation fits those assumptions.