Appellate courts do not retry the case, nor do they listen to new evidence. They only consider the facts and evidence presented during the trial.
Appellate courts normally are required to give great weight to the factual findings of the trial court (or the jury). Appellate courts typically can only overturn findings of fact if the trial court came to a conclusion that no reasonable person would have reached. Further, the court of appeal court will only overturn the decision if the error was so prejudicial that there is a reasonable chance that the error changed the outcome of the trial.
The stronger arguments on appeal are attacks on the procedures the trial court used or arguments that the trial court wrongly interpreted the applicable law. These matters are typically reviewed de novo, meaning the higher court gives the trial court no deference. For example, courts of appeal review the lower court's interpretations of statutes and constitutions de novo.