definitions as explanations

Of course, since we have a definition for truth and since every definition enables us to replace the definiendum by its definiens, an elimination of the term "true" in its semantic sense is always theoretically possible... Some people have therefore urged that the term "true" in the semantic sense can always be eliminated, and that for this reason the semantic conception of truth is altogether sterile and useless... If, however, anyone continues to urge that — because of the theoretical possibility of eliminating the word "true" on the basis of its definition — the concept of truth is sterile, he must accept the further conclusion that all defined notions are sterile. But this outcome is so absurd and so unsound historically that any comment on it is unnecessary. In fact, I am rather inclined to agree with those who maintain that the moments of greatest creative advancement in science frequently coincide with the introduction of new notions by means of definition.

Tarski - The Semantic Conception of Truth

Definitions form the building blocks of theorems. If you can pinpoint the correct ones, then you are more likely to get interesting deductions. That is why good definitions advance science.

Definitions by themselves have no intrinsic value. They are nothing but labels attached to some collection of mathematical sentences and physical phenomena. That is why a computer will never find the introduction of a new definition illuminating.

Definition are not explanations, but the good ones can give the sensation of an explanation. For instance, more than half of this Wikipedia article consists of definitions. Nevertheless it is extremely illuminating!