A more thorough explanation:

The dominant-jurisdiction principle is a rule that states that the court in which a case is first filed maintains the suit, to the exclusion of all other courts that would also have jurisdiction.

For example, if a person files a lawsuit in a state court, and the defendant later files a similar lawsuit in a federal court, the state court would maintain the case because it was the court in which the case was first filed.

This principle is important because it helps to prevent multiple courts from hearing the same case, which can lead to conflicting decisions and waste of resources. It also ensures that the court that is most familiar with the case and the parties involved is the one that hears the case.