(Warning: this is a primer, oversimplifications ahead.)
Various people have brought different lawsuits against Donald Trump and his administration, claiming the unconstitutionality and illegality of Trump’s executive orders restricting travel, colloquially known as “the Muslim ban.” Because these lawsuits raise federal constitutional questions and claim Trump has violated federal statutes, the cases have all been brought in federal court. But there isn’t just one big “federal court.” There is the federal court system. It has both a horizontal and a vertical dimension. Horizontally, the federal judicial system is divided into circuits and then sub-circuits. When a plaintiff sues in federal court, she starts in a trial court in a particular sub-circuit. Which one usually depends upon either where she resides or where the injury she is alleging happened. When a cause of harm manifests in many places-like a nationwide ban on immigration ordered by the President-it often triggers multiple suits, each one brought by a different plaintiff or group of plaintiffs seeking relief for the specific injury the harmful conduct has caused her or them. Because of differences in the factual circumstances and differences in the legal theories each plaintiff sues upon, the initial trial court decisions at the horizontal level will vary in meaning even if all of them temporarily restrain the governmental action in question.
As trial court orders are appealed, the vertical dimension of the federal judicial system kicks in. A federal district court judge’s decision can be appealed. If it is, the case is generally reviewed by a panel or subset of that district’s appellate judges. For example, a decision of the court in the Western District of Washington, in Seattle, can be appealed to the Ninth Circuit (not every trial court order or decision is immediately appealable, but for purposes of this discussion, I am oversimplifying). When that subset or panel rules, the losing party can request review of the entire group of appellate judges for the circuit (en banc). Finally, a party who loses a case upon en banc review can petition for review by the U.S. Supreme Court. There is no right to Supreme Court review. The Court decides whether to take any given case.
In a situation like the current one, where the losing party (Trump in his official capacity and the Executive Branch officials implementing the orders) is the same across the original trial court orders, whether and which vertical next moves are made are the choice of the losing party. The Department of Justice, which represents the Executive Branch of the U.S. Government, has to decide which orders to appeal, considering the content or significance of an individual case and the likelihood of winning on appeal. So far, Trump’s DOJ has fought, and won, one effort to renew a TRO (not an appeal of the original TRO), in Massachusetts; and today has decided to appeal the most wide-reaching and, in my opinion, forceful ruling staying the executive orders, which was issued in Seattle, by the Judge James Robart of the Western District of Washington State. Judge Robart had scheduled argument as to whether to make the temporary restraining order permanent, but since the Executive Branch has decided to appeal the temporary order those arguments may be postponed.
Meanwhile, the government may file appeals in other cases in circuits other than the Ninth , and the plaintiffs in Massachusetts (who lost the renewal of the TRO) may decide to appeal that ruling. If there are simultaneous appeals proceeding vertically, the different circuits could end up with different results on the constitutionality or legality of the Executive Orders, in what is called a circuit split. Sometimes the Supreme Court decides to consolidate several appeals from the circuits to resolve a split, sometimes the Court chooses one case because deciding it would effectively decide the split, and in some instances (though certainly not this one), the Supreme Court does not resolve a circuit split, meaning that the opinions of the appellate courts in each circuit control the law in that circuit.
Scholars and analysts have much to say about the pros and cons of the horizontal and the vertical dimensions of the federal judiciary. Setting aside these larger debates, what matters for now is whether there will be a relatively quick decision at the appellate level of any circuit and then whether the loser will appeal the case to the Supreme Court and then whether the Supreme Court takes that case or waits to see what, if any, splits or consensus emerges among the various circuits.
Should Trump withdraw the Executive Orders or should Congress take action to negate them, the current wave of lawsuits would stop or stall. The federal courts would not become involved again unless or until the Executive promulgated new orders which could be litigated or the Executive chose to challenge the constitutionality of any Congressional action that might be taken.