Before describing in detail the individual courts in the labyrinthine state court system, it is important to introduce a few terms related to judicial jurisdiction.
In the court system, there are two types of jurisdiction: original jurisdiction and appellate jurisdiction. Original jurisdiction is the authority of a court to provide the first hearing of a specific case. As you'll see below, several courts in the Texas system have original jurisdiction, but only in specific types of cases (e.g., misdemeanors, felonies). When two different types of courts have original jurisdiction in the same type of case, they are said to have concurrent jurisdiction.
Other courts have no power of original jurisdiction regardless of the type of case. Instead, they have appellate jurisdiction, or the authority to hear appeals of cases that were originally tried in other (lower level) courts. The American legal tradition allows for review - or appeal - of cases that were tried and concluded in courts of original jurisdiction. This internal check within the judicial branch recognizes that no system is infallible and that cases can be complex. A system that allows review will in theory discover errors and reduce injustices - unless there are biases built into the judicial system.
During the appeal process, no new facts or evidence may be introduced. Questions of fact are assumed to have been decided in favor of the victor in the trial court. Instead, the appeals court usually examines only the record of the trial. If it is a criminal case, the conduct of law enforcement personnel and procedures are also included in the review. This is a critical point, because it means that the court that originally heard the case must be a "court of record" - meaning that the court must keep an official record of the proceedings, an expensive requirement. Without records it would be impossible to review the proceedings of a case.
In Texas most of the local trial courts of limited jurisdiction are not courts of record. The Justice of the Peace courts and many Municipal courts do not have court reporters that produce a transcript of the trial. Consequently, appeals from these courts take the form of a trial de novo, a completely new trial in which evidence and testimony are presented all over again.
For a diagram of the original and appellate jurisdictions of the various courts in the Texas judicial system, see this chapter's feature The Court Structure of Texas.