If the verdict of the jury goes against you, you may have the right to an appeal to a higher court. This is true whether you are the plaintiff or the defendant. In order to appeal, there must be an error of law by the judge. This may be a ruling on evidence questions, or motions, or jury instructions. However, it is important to remember that in general you cannot appeal the findings of fact made by a jury.
Appellate procedures differ considerably between jurisdictions.
In general, it is a process by which legal arguments are made in written documents called briefs, then argued orally before the appropriate appellate court. The record consists of the evidence, the exhibits, and any other proceedings taken down by the court reporter.