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Most civil and criminal decisions of a state or federal trial court (as well as administrative decisions by agencies) are subject to review by an appeals court. Whether the appeal concerns a judge's order or a jury's verdict, an appeals court reviews what happened in prior proceedings for any errors of law. This means losing parties can't appeal a case just because they're unhappy with the outcome; they may only challenge decisions that may have resulted from errors, such as a misinterpretation of legal precedent or reliance on evidence that should have been excluded.
If you're appealing a court decision or judgment, you'll want to get a handle on how the process works. The following is an overview of court appeals.
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Appellate Briefs
The main form of persuasion on appeal is the written appellate brief, filed by counsel for each party. With this brief, the party that lost in the trial court will argue that the trial judge incorrectly applied the law. The party that won below will argue that the trial court's decision was correct. Both parties will support their positions with reference to applicable case law and statutes.