I founds a great synopsis on the Indiana state court website:
There are three major differences between trial-level courts and appellate-level courts:
- witnesses and exhibits,
- judges, and
Trial courts are the courts where cases start. In the trial court, both sides present evidence to show their version of what happened. Most of the evidence presented in the trial court comes from witnesses (people who answer questions relating to the case) and exhibits (items and documents connected to the case, such as pictures, clothes, weapons, papers, etc.). However, in the appellate courts, there are no witnesses, and no evidence is presented. In appellate courts, the lawyers simply argue legal and policy issues before the judge or a group of judges. In the trial courts, the lawyers present evidence and legal arguments to persuade the jury in a jury trial or the judge in a bench trial.
The second difference between the two courts is the judges. In trial courts, there is one judge in the courtroom. That judge decides what evidence can and cannot be used and often decides the outcome of the case. In most jurisdictions, appeals are decided by more then one judge.
The last major difference between the trial courts and the appellate courts is the role of the jury. A jury is a group of citizens who listen to the facts and make decisions about the case. A jury is sometimes used in trial courts to help decide the case. In a criminal trial, the jury decides whether a person is guilty or not guilty. A criminal trial involves the government (the state of Indiana, for example) bringing charges against someone who committed a crime, such as robbery, murder, or drunk driving. In a civil trial, the jury decides whether a person is liable (legally responsible for damages) or not liable (not responsible). Individuals or companies who cannot settle a dispute file a document called a complaint to start a civil trial. Divorce, car accidents, and traffic violations are some of the most common types of civil cases. There can be a jury in either a civil or criminal trial. However, there is no jury in the appellate courts. Appellate judges determine the outcome of all appeals.
A big misunderstanding about the appellate courts is that they simply rehear the case over again, evidence and all. But the truth is that appellate courts do not rehear the facts of the case. Appellate courts focus on questions of law, NOT on questions of facts like the trial courts. The appellate judges want to know whether the law was applied accurately.
The appellate court overrules a trial court decision only if a very important legal error was made in the trial court. In some cases, the appellate court judges might believe that the outcome of the trial court should have been different, but if no legal errors were made, they will not overrule the lower court. The appellate judges make their decisions based only on legal arguments of how the law should be applied and interpreted.