According to About.com. concurring opinions are written by associate court justices who agree with the majority opinion on a given case, but for somewhat different reasons than the rest of the majority. Dissenting opinions are written by justices who are not in the majority and wish to publicly disagree with the ruling of the court. In many instances, concurring opinions are actually dissenting opinions in disguise.
About.com explains that the majority opinion is an explanation of the reasoning behind the majority decision of a supreme court. Even when a justice agrees with the majority decision, however, there will sometimes be more than one opinion issued in the case. Justices on the panel who disagree with the majority decision often write dissenting opinions that explain their reasons for opposing the ruling of the court. When a justice agrees with the verdict but begs to differ on the logic that led to it, a separate, concurring opinion may be written to explain a matter of law relevant to the case. Once the opinions have been written, the other judges on the panel are generally free to just sign their names to one or the other opinion as a way of endorsing either argument.