An agreed statement is a summary of the trial court proceedings that all the parties have agreed to. An agreed statement can be used instead of a clerk's transcript for a record of documents in the trial court proceedings if it includes copies of the documents that must be in a clerk's transcript. It can also be used for the record of oral proceedings in the trial court (instead of the reporter's transcript).
Read rule 8.836 of the California Rules of Court and Information on Appeal Procedures for Limited Civil Cases
Read rule 8.134 of the California Rules of Court for details on how to prepare an agreed statement in the Court of Appeal (for unlimited civil cases).