Explanations

The explanation tells us how to rationally generalize from the details of the correct training example to a correct general hypothesis.
Namely, the features of the training example that are mentioned in the explanation are the ones that should be included in the hypothesis.
What is the prior knowledge needed in the chess example?
The knowledge about the legal moves of chess, the fact that players alternate moves, and the goal is to capture the king.
Note that, in principle we could use this knowledge to calculate the optimal move for every board, but this is not practical in most situations (cf. deep blue).