The Sacred Roman Rota is essentially the supreme court of the Catholic Church (I will explain the "essentially" later).
It has two main functions:
The origin of its name (Rota, Latin for wheel) is not quite clear. Some think it has to do with the fact that the Rota judges sit at a round table.
But it is more likely a reference to how the court works. The judges are appointed by the Pope. There are 12 judges hearing a case. But there are more than 12 members of the Rota. They are assigned to each case like a queue. For each new case, one judge is taken off one end of the queue, another one is added at the other end.
The Rota's first function, as appellate court, is what it does most often. The Catholic Church has an entire legal system. The most common legal cases handled by church courts in the US are marriage annulment cases. In other countries, there may be other cases as well. It depends pretty much on the relationship between the Church and the State.
Each diocese (run by a bishop) has a court. Its decisions can be appealed to the court of the archdiocese, etc, all the way to the Rota.
I said the Rota was essentially the supreme court. But it is possible to appeal against its decision. One can either appeal directly to the Pope, or, well, to the Rota. Because the judges rotate, it is possible to have an appellate court which is not the same as the previous Rota. Theoretically, one may keep appealing forever.
Now, no canonist in his right mind would ever appeal his case to the Pope. Why? Because Pope's decisions are final and irrerversible. Roma locuta, causa finita. Now, that may be nice if the Pope rules in your favor, but what if he does not? It is definitely not a risk worth taking.
First of all, not every Pope is a canonist. For example, John Paul II is definitely not one (he is a philosopher). Secondly, even at times when the current Pope happens to be a canonist, the Pope is a rather busy man. He cannot spend too much time on a case. Hence the risk of a final decision without appeal is not, well, appealing...
The second function of the Rota is to clarify the meaning of the law. Any Catholic, not just the canonists, has the right to ask the Rota for a clarification.
As a matter of fact, a canonist is the last person to ask for a clarification. Why should he? He is the expert, and the Code of Canon Law explicitly states it is to be interpreted by experts. But once the Rota has made an interpretation, the canonists have no choice but to accept that interpretation.
It is, however, possible to ask the Rota to interpret a law the Rota has already interpreted before. And they can interpret it differently. It happens rarely, but it does happen. So a canonist might ask the Rota to interpret the law that was already interpreted in the hope they would change the interpretation, but never one they have not interpreted in the past.
Of course, since anyone (or at least any Catholic) can ask, canonists cannot stop other Catholics from asking. But it is generally not a good idea.
Here is an example why: For centuries, Catholics were allowed to receive communion at most once a day. After Vatican II the law was changed. Catholics were now allowed to receive communion even if they had already received it that day.
Now, every canonist in the world interpreted it to mean one can receive communion an unlimited number of times during the same day. Not during the same mass, mind you, but should one attend 10 masses on the same day, one could receive 10 communions.
But someone just had to ask. And the Rota said no, the law means one can receive communion a second time, but not a third time on the same day. Much to the dismay of canonists and many devout Catholics the law was made more restrictive.
Disclaimer: While technically I am a Canonist (I have a JCL from the Gregorian University), I have not followed the developments in Rota's decisions for the last ten years, so I cannot say if that restriction is still in place. If you are a Catholic and like to receive communion more than twice a day, please do not make this write-up stop you. If in doubt, ask your priest. Actually, the decision was so unpopular, many priests chose not to mention it to their congregations, preferring a don't ask, don't tell policy. | 
