A majority opinion is reached when more than half of the justices that constitute a specific court agree on a certain judicial opinion or decision.
A majority opinion is not necessarily reached in all the cases that are discussed at court. For instance, sometimes, when a majority decision is being voted, opinions to support the same vote might drastically differ from each other, and the justices cannot agree on the same set of reasons. In such cases, several concurring opinions are registered, even tough none of them represents the majority of the justices in the room. In this case a plurality opinion has been reached, instead of a majority opinion.