In the simple case, explicit reasoning is reasoning which:
"What do I mean by explicit reason? I don’t refer merely to “System 2”, the brain’s slow, sequential, analytical, fully conscious, and effortful mode of cognition. I refer to the informed application of this type of thinking. Gathering data with real effort to find out, crunching the numbers with a grasp of the math, modeling the world with testable predictions, reflection on your thinking with an awareness of biases. Reason requires good inputs and a lot of effort." - Jacob Falkovich, The Treacherous Path to Rationality
However, the exact definition may vary based on context. For example, explicit reasoning might be operationalized as imaginary verbal reasoning taking place in a person's inner monologue (ie, in auditory working memory). In other cases, we might have a much higher standard, eg actual symbolic logic written on an external medium such as paper. So, reasoning can be more and less explicit, along several dimensions....