What does a rectifier regulator do in a lawn mower?

Your lawnmower engine has an alternator, which creates an supply of AC current. Your battery, and most electrical components, all require DC power. The rectifier acts as a one-way check valve to chop off the negative half of the electrical sine wave to create DC power. The regulator adjusts amperage to match the needs of the electrical system (e.g. if the battery is fully charged and the lights are off, it reduces current flow. If the battery needs juice and you're running lights or electrical goodies, it opens the gates).