Inferential distance is a gap between the background knowledge and epistemology of a person trying to explain an idea, and the background knowledge and epistemology of the person trying to understand it.
For example, explaining the evidence for the theory of evolution to a physicist would be easy; even if the physicist didn't already know about evolution, they would understand the concepts of evidence, Occam's razor, naturalistic explanations, and the general orderly nature of the universe. Explaining the evidence for the theory of evolution to someone without a science background would be much harder. Before even mentioning the specific evidence for evolution, you would have to explain the concept of evidence, why some kinds of evidence are more valuable than others, what does and doesn't count as evidence, and so on. This would be unlikely to work during a short conversation.
There is a short inferential distance between you and the physicist; there is a very long inferential distance between you and the person without any science background. Many members of Less Wrong believe that expecting short inferential distances is a classic error. It is also a very difficult problem to solve, since most people will feel offended if you explicitly say that there is too great an inferential distance between you to explain a theory properly. Some people have attempted to explain this through evolutionary psychology: in the ancestral environment, there was minimal difference in knowledge between people, and therefore no need to worry about inferential distances....