Full Idea
The three types of explanation are 'epistemic' (the event is expectable because of a law), or 'modal' (the event is necessary because of a law), or 'ontic' (it is shown how the event fits into the world's causal structure).
Gist of Idea
Explanation is either showing predictability, or showing necessity, or showing causal relations
Source
Stathis Psillos (Causation and Explanation [2002], §11.1)
Book Reference
Psillos,Stathis: 'Causation and Explanation' [Acumen 2002], p.281
A Reaction
Prediction, necessity or causes. It is hard to think of any other way to explain something. Presumably you would exclude necessities if you didn't believe in them. Hume would go for prediction, on the basis of regularities. Personally, I want it all.