In many ways, they are the work and they are the effects. American legal education, especially in the first year of the three, is largely an exercise in analyzing and extrapolating from these opinions.

The opinions of the court announce the decision, but they also declare the reasoning, which determines how it will apply to similar situations not under litigation, sometimes pretty formally and possibly even with bright-line limitations. They also reveal the court's thinking, inviting people to pursue similar logic in cases they may file.

For more complex cases, an opinion will even set some of this out in a test with specific steps in the analysis, or with certain required elements to apply (e.g. Miranda warnings). There was a recent case that will likely be hugely influential where some guy got his civil penalty undone, but the real meat of it is that the majority opinion said that federal regulatory agencies have no power to interpret their own subject matter, and instead must defer all ambiguities to judges. Maybe good from time to time, such as when utterly unqualified boors are running the agencies, but generally this is going to make it very difficult for government to be effective, and it comes specifically from what's in the opinion.

Even dissenting opinions can be important, outlining the opposing way of thinking and sitting there ready to be used if a similar question comes before a court with a different generational or political makeup.