The carburetors on inboard mounted gasoline engines must be equipped with an approved back-fire flame arrestor. what purpose does having a back-fire flame arrestor play?

Back-fire flame arrestors are preventive measures to avoid catastrophic events. They are made to prevent the ignition of gasoline vapors if ever the machine engine malfunctions and backfires. They are similar logically to check valves which prevent backflow of fluids to avoid contamination, or in this case, avoid accidents.