I'm going to give a bit more nuanced answer.
To begin, if you are going to read many programming language theory and related research papers, get used to the phrase "by structural induction". It's not uncommon that these three words are the entirety of a proof sketch in a paper. The majority of proofs in this area are very boring but also tedious. So boring and tedious that we've written programs to write these proofs for us. If a computer can quickly find these proofs fully formally with a one-line proof script, this elliptical style is moderately justified.
Sometimes an author will say that you can find a proof by "following your nose". This means that the structure of the theorem strongly suggests one (or at most a few) next steps. This (combined with some searching) is what's behind Coq's
auto tactic, Agda's Agsy tool, and the Djinn tool. Structural induction is the "follow your nose" step you get when faced with the problem of proving something about all members of an inductively defined type like an abstract syntax tree. So an elliptical "by structural induction" is really the statement of "do the obvious thing; there are no surprises".