The U.S. Supreme Court decides cases by majority vote; more than half of the justices participating must vote in favor of the decision. If the justices in the majority agree to sign a single opinion, they produce a majority opinion for the Court. Now and then, however, there are so many individual concurring opinions that the opinion that garners the most votes is called not a majority opinion but a plurality opinion.
For example, in Dennis v. United States (1951), the Court decided the case by a vote of 6 to 2 (one justice did not participate). Two justices wrote separate concurring opinions and thereby made it impossible for there to be a single majority opinion for the Court. Instead, there was a plurality opinion (signed by four justices), supported in many respects by two justices' concurring opinions, and opposed by the other two justices' dissenting opinions. Thus, Chief Justice Vinson announced the decision of the Court based on a plurality opinion.