Cases heard by the United States Supreme Court are decided by a majority vote. A single justice then writes the opinion of the case, which announces the decision and explains the legal reasoning for arriving at that outcome. Justices who agree with that opinion simply attach their names to it. A justice who agrees with the outcome but disagrees with the legal reasoning can write a concurring opinion. Those who disagree with the outcome can write a dissenting opinion.
The majority opinion, also known as the opinion of the court, represents the view of the majority of the justices hearing the case. The legal reasoning that forms the opinion explains the law and its application to a specific case and gives guidance on the interpretation and application of laws.
A dissenting opinion is an opinion written by a justice who voted in the minority. The dissenting opinion explains why the dissenting justice disagrees with the outcome and reasoning of the majority of the court. Since the dissenting opinion represents the minority position, the reasoning is not binding precedent. However, the dissenting opinion offers valuable insight into the deliberative process behind a case and articulates reasoning that future court cases could revisit.
A concurring opinion agrees with the outcome of the majority opinion but not necessarily the reasoning found in the majority opinion. The concurring opinion gives a concurring justice an opportunity to further explain the legal reasoning of a case or to offer a completely different legal reasoning for the decision.
A plurality opinion announces the decision of the court but fails to get a majority of the justices to support the legal reasoning. When no single opinion gets majority support, the decision that gets the most votes and supports the majority outcome becomes the plurality opinion. Since the legal reasoning is not adopted by a majority of the justices, it is less reliable as legal precedent.