Final answer:
A Supreme Court justice who disagrees with the majority and provides their own reasons is offering a dissenting opinion, which is significant in the judicial system for affecting future cases and offering different perspectives within the Court.
Step-by-step explanation:
When a justice of the Supreme Court disagrees with the majority's decision and provides an opinion explaining the reasons behind their disagreement, this action is best described as a dissent. A dissenting opinion is significant in the judicial process because it often includes legal reasoning that can influence future cases and may eventually contribute to overturning established precedent. It also gives insight into the different perspectives within the Supreme Court regarding the case at hand. A dissenting opinion stands in contrast to the majority opinion, which represents the view of more than half the justices on the Supreme Court and forms the basis for the final decision in a case.