Knowledge of how the justices work.
The way that the Court and every one of the justices work is that he/she will draft out with the clerks the broad principles and approach that he/she wishes the decision to be crafted around. Which cases influence the precedent, which regulations take what role in the decision, what issues to "turn" the case on, etc.
It's the job of the clerks then to go research, summarize, and create the bulk of justice's position based on knowledge of the details. They (justice + clerks) then review and talk about the evolving draft opinion several times over the course of months, circulating drafts to the other justices (and their clerks) as well. And note, most of the facts/issues already came up in the lower courts cases and rulings, so there has already been some fair surfacing of the details of the dispute (and what other judges believe the important issues to be) as it made its way through the system.
The justices have many opinions per term to do this for, and you can be very sure that while the "authoring" justice has been briefed on (and very well has tested the ideas with the clerks in detail), the summary of how APIs work and their legal status is not based on the justice him/herself wading through license agreements and "figuring out" the structure of the code or its legal status.
So, that is not to say that the justices are ignorant of the details (far from it), but the level of detail needed to form the groundwork of the opinion is heavily shouldered and created by the law clerks. But the main conclusions of the opinion are definitely of the justice him/herself (with input from the clerks).
-- By the way, the clerks (you may not realize) already have had a role in getting the case even to be heard before the Supreme Court, in briefing and summarizing the underlying appealed case on why it should be ripe for a decision, so they already many of the issues at stake and how to think about them.
Maybe think of it like a software engineering manager and the individual developer. The manager can lay out the principles by which a certain piece of code is to be written, and the capable developer will identify all the issues, test cases, etc., and they will review it together at various stages. You would not say that either could have done it without the other. It's kind of like that (when software engineering works like it should).