When someone believes that they have been convicted of a crime unjustly or that the punishment is harsher than it should be, they have the ability to appeal this to a second court. This second court will look at the facts of the case to determine whether the decision of the first court was correct or if the decision should be overturned. This is a complicated process.
The appeal process all starts with hiring some kind of legal party to defend you in this case. They can prepare a written opening brief that is meant to present an argument for why the court should overturn a court decision. This brief is even more important for cases that are being submitted to the Supreme Court because this court is selective on the cases they take.