Computational processes are increasingly more powerful and complex but also more difficult to understand by humans. Considering that Natural Language is a suitable tool for describing human perceptions, building self-explanatory computational systems ready to communicate with humans in Natural Language becomes a hot challenge. Based on
ideas taken from Cognitive Science, we propose a novel model to facilitate achieving this goal. We consider the computer as a metaphor of the mind and we use references from Philosophy, Neurology, Linguistics, Anthropology and Sociology to provide a structure of different components that allow coping with the complexity of generating linguistic de-
scriptions about computational processes. We illustrate the use of this model with several examples.