In Pennsylvania, as in many states, there are several different levels of courts. Pennsylvania has four: Special Courts, the Court of Common Pleas, the Superior Court, and the Supreme Court. There's another court, the Commonwealth Court, that exclusively deals with cases where the plaintiff or defendant is the state itself.
Special Courts deal with minor violations, and includes things like minor civil cases and traffic court.
The Court of Common Pleas includes family law cases, like divorce, child custody, and child emancipation, along with most major civil and criminal trials, and anything that was appealed from the lower Special Courts.
The Superior Court hears appealed cases from the Court of Common Pleas, including family law cases and criminal trials.
The Supreme Court of the state is similar to the Supreme Court of the United States. It has just a few justices--in this case 7, rather than the US Supreme Court's 9--and they are the highest appeals court in the state. Like the US Supreme Court, the PA Supreme Court can choose whether to take on appeals from the lower courts, except in certain cases, like capital punishment rulings, where the rules are a bit different.
In some states, judges are appointed, usually by a governor, but in Pennsylvania appelate court judges are elected for 10-year terms.
For a great summary of major issues and court battles defining the boundaries of state and federal power, check out eNotes' own article "Federalism and State Powers", linked below.