In the federal court system of the United States, the two main types of courts are district courts and circuit courts. The district court is where any trial would start in a case that involves federal laws. The circuit courts are the first level of appeal, if someone appeals the decision reached in district court.
There is actually a third level -- but only one court at the third level. The Supreme Court of the United States exists as the final place for appealing a case, after decisions at the circuit court level.