A court of record is a trial court or appellate court in which a record of the proceedings is captured and preserved, for the possibility of appeal. A court clerk or a court reporter takes down a record of oral proceedings. That written record (and all other evidence) is preserved at least long enough for all appeals to be exhausted, or for some further period of time provided by law (for example, in some U.S. states, death penalty statutes provide that all evidence must be preserved for an extended period of time).
Most courts of record have rules of procedure (see rules of evidence, rules of civil procedure, and rules of criminal procedure) and therefore they require that most parties be represented by counsel (specifically, attorneys holding a license to practice law before the specific tribunal).
