A dissenting opinion is where a judge explains why she disagrees with the conclusions reached by a majority of the court.  In the United States appellate courts sit as a panel of at least three judges.  Let’s say an appellate court meets to decide whether a trial court judge made the right decision.  If two judges decide the trial court made the right decision then the appellate court will affirm the trial court’s decision.  The third judge, who disagrees with the other judges, can write an opinion in which she explains why she disagrees.  Her explanation as to why she disagrees is a dissenting opinion.