Explanations give causes. Explaining something, whether that something is particular or general, gives something else upon which the first thing depends for its existence, or for being the way that it is. The bomb explosion explains the plane crash; the statistics relating smoking and heart disease are explained by the mechanisms that connect the ingestion of cigarette smoke with effects on the blood vessels of the heart. Often in science, explanations are given for empirical generalizations, the explanations appealing to a 'deeper' level of structure and mechanism. Why does it grow cold in the winter? Because the sun, being lower in the sky, and the sunís light striking at a lower angle, warms the earth less. Explainer and Explained may be general or particular, and accordingly, 'inference to the best explanation' may apply to generals or particulars.
The draft report mentions the question of the relation between explanation and prediction. It is tempting to think that they have 'opposite chronology,' predictions projecting forward in time and explanations projecting backwards, but I think that time is not the essence of the matter. The temporal asymmetry results when explanation and prediction are based on mechanical or 'efficient causation' (Aristotle, rendered into English). For other forms of causation, say, teleological or final cause, explanations proceed from effect to cause, and predictions may proceed from cause to effect, but the simple temporal asymmetry is lost. For example, the existence of the spout on the teapot may be explained by its purpose for pouring tea, and the need for some means of pouring predicts the existence of something like the spout. Even for efficient causation, the cause and effect may be simultaneous, such as for 'sustaining causes.' The heater & thermostat maintain the temperature of the room. The temperature of the room is explained by the existence and operation of the heater & thermostat; the proper operation of the heater & thermostat predict the temperature of the room; but all occur simultaneously.
Note, too, that while predictions are often based on reasoning from cause to effect, that is not the only way in which predictions may be licensed. For example I predict the weather tomorrow by appealing to the authority of the weatherman, without knowing about the causes.