What is an explanation?
We start from an intuition about the relationship between a proposition and a phenomenon.
For example, regarding the phenomenon "car crash." We notice a pattern in which the proposition "the driver was drunk" relates to the car crash phenomenon in a way that "apple pie was in the trunk" does not.
Another example, regarding the phenomenon that the "floor is slippery." We notice that "floor is brown" does not relate to the slippery floor phenomenon in the same way as "floor is wet."
We call this relation "explanation." This is our starting point. It is the primary intuition that there are explanatory relations.
The next step is to try to devise a formal definition of an explanation. Our formal definition should account for why "drunk driver" explains "car crash", but "pie in trunk" does not. Though our formal definition may be inspired by intuition, our definition should work without direct reference to intuition when examining any particular case.
In devising a formal definition of explanation, we must account for other intuitions about explanations.
First, it is intuitive that not everything is explained. If everything were explained, we wouldn't need or notice or search-for explanations. There is a distinction to be made. Some things are unexplained.
Second, I think it is intuitive that "car crash" does not explain "car crash". Restating the phenomenon does not make an explanation.
Third, it is intuitive that there must be some relevancy between the explanation and what is being explained.
These intuitions can come into conflict.
Our gut might tell us that "X explains Y, where X is defined as that which explains Y." However, this gut instinct would contradict the other intuition that trivialities are not explanatory. Upon reflection, we see that X merely labels the explanation without saying what it actually is.
This conflict is one reason why we want formal definitions of explanation. The idea is that we can at least classify explanations into types according to their conformance with all of our intuitions.
My claim is that the triviality intuition is more important than the primary intuition. The primary intuition tells us that there is a distinction, but the other intuitions tell us more specifically what isn't an explanation.
If we accept trivial explanations, we are saying that everything is at least a little bit explained automatically just by restating what it is we're explaining. I think we would be fooling ourselves if we accepted trivialities as explanations.
This is why prediction is a good formal criterion for explanation. It demands that an explanation be relevant to the observations by predicting them, and demands that the explanation not be a restatement of our observations. It also accounts for the fact that some phenomena remain unexplained because we lack predictive models of those phenomena.