A "statement on appeal" (the name used in limited civil cases) or "settled statement" (the name used in unlimited civil cases) is a summary of the trial court proceedings that is approved by the trial court. In limited civil cases, a statement on appeal can be used for the record of oral proceedings (what was said in the trial court) if the appellant chooses this option. This option is often used when the trial court proceedings were not recorded by either a court reporter or official electronic recording equipment.
In unlimited civil cases, a settled statement can be used for the record of documents from the trial court proceedings, but only after you get the trial court's permission.
Read California Rule of Court 8.137 for details on how to prepare a settled statement.