From IFWiki

Formally, the commands needed to resolve a puzzle or win a whole game. In the case of a whole game, this sort of solution is synonymous with a walkthrough.

"Solution" is also the process of understanding a previously inexplciable world. In this sense, the solution is not just the series of commands needed, but a working understanding of the world. Someone who have sovled a puzzle in this sense can explain not only what commands to type by why the puzzle works the way it does.