When you take your court case to a person after you have already lost a case and been convicted, they take on the responsibility of looking at this case and determining what can be done better on appeal to get a reduced sentence or even to get charges dropped completely. This takes a lot of evaluation of the case. It may also include a study of similar cases.
A person looking over a case after conviction might look closely at what went wrong in the defense, what evidence was presented and whether the punishment fit the crime. They can do some case study research to see what the results of similar cases were and how these differed. By looking at all of this information, they can help build a stronger case to use on appeal.