Explanation: An explanation of something described by a set of statements S is a set of statements that deductively entails S.
This is a convenient definition because it implies that explanations can be supported and refuted by their consequences. It is a bit strict in that many explanations that are at least practically sufficient are given in terms of analogies or leave much open to be filled in by proper understanding.
Explanations need not be known to be true and indeed need not be true to be perfectly good explanations. Similarly, they need not be believed whether they are true or not.
And many explanations, or attempted explanations, do not get much farther than a suggestion of a possible cause, either because the suggestion is supposed to lead nowhere, or a better explanation is found.