As a learning process, "self-explanation" is defined as:
A self-generated explanation of presented instruction that integrates the presented information with background knowledge and fills in tacit inferences.
Another definition from Roy, M., & Chi, M.T.H. (2005). The self-explanation principle. In R.E. Mayer (Ed.) Cambridge Handbook of Multimedia Learning:
Self-explanation is a domain general constructive activity that engages students in active learning and insures that learners attended to the material in a meaningful way while effectively monitoring their evolving understanding. Several key cognitive mechanisms are involved in this process including generating inferences to fill in missing information, integrating information within the study materials, integrating new information with prior knowledge, and monitoring and repairing faulty knowledge.
As an observable student activity, "self-explanation" is defined as:
Operationally, self-explanations are detected by asking students to speak aloud as they study and counting any utterance beyond paraphrasing material as a possible self-explanation
Also see Chi, M.T.H., et al (1989).Self-explanations: How students study and use examples in learning to solve problems. Cognitive Science, 15, 145-182.