Almost all of the cases that the Supreme Court hears are cases that are on appeal. The Supreme Court does have original jurisdiction over a very few cases, but these are quite rare. This means that the Supreme Court is almost always hearing cases where only matters of law are at issue (rather than matters of fact). The Supreme Court is simply, in those cases, trying to decide if the law (whether statute law or the Constitution) has been correctly applied.
Cases heard by the Supreme Court generally involve very important and difficult issues of law. Cases that are not important, or where the law is obvious, do not make it all the way up the ladder to the Supreme Court.
So, the cases the Court hears are those that involve important and difficult questions of law. It hears those cases either after they have come up through the federal court system or after they have been decided by the supreme court of a state.