Abstract: Many self-adaptive systems benefit from human involvement and oversight, where a human operator can provide expertise not available to the system and detect problems that the system is unaware of. One way of achieving this synergy is by placing the human operator on the loop - i. e., providing supervisory oversight and intervening in the case of questionable adaptation decisions. To make such interaction effective, an explanation can play an important role in allowing the human operator to understand why the system is making certain decisions and improve the level of knowledge that the operator has about the system. This, in turn, may improve the operator's capability to intervene and if necessarily, override the decisions being made by the system. However, explanations may incur costs, in terms of delay in actions and the possibility that a human may make a bad judgement. Hence, it is not always obvious whether an explanation will improve overall utility and, if so, what kind of explanation should be provided to the operator. In this work, we define a formal framework for reasoning about explanations of adaptive system behaviors and the conditions under which they are warranted. Specifically, we characterize explanations in terms of explanation content, effect, and cost. We then present a dynamic system adaptation approach that leverages a probabilistic reasoning technique to determine when an explanation should be used in order to improve overall system utility. We evaluate our explanation framework in the context of a realistic industrial control system with adaptive behaviors.