Insights from cognitive science about how people understand explanations can be instructive for the development of robust, user-centred explanations in eXplainable Artificial Intelligence (XAI). I survey key tendencies that people exhibit when they construct explanations and make inferences from them, of relevance to the provision of automated explanations for decisions by AI systems. I first review experimental discoveries of some tendencies people exhibit when they construct explanations, including evidence on the illusion of explanatory depth, intuitive versus reflective explanations, and explanatory stances. I then consider discoveries of how people reason about causal explanations, including evidence on inference suppression, causal discounting, and explanation simplicity. I argue that central to the XAI endeavor is the requirement that automated explanations provided by an AI system should make sense to human users.