Most of the L-Jetronic systems as fitted to our air-cooled Volkswagens don't have an oxygen sensor. However, many of the California models do, so I will cover it here. The oxygen sensor's main purpose is to give feedback on how the engine is running to the ECU, which can then correct any problems. Mainly, the oxygen sensor tells the ECU about fuel/air mixture and allows the ECU to keep the fuel/air mixture precise.
The oxygen sensor is mounted in the exhaust system, usually close to the catalytic converter. The oxygen sensor has to be mounted in a part of the exhaust system that heats up quickly. The oxygen sensor does not work until it reaches about 600 degrees F. When it gets to 600 degrees, it becomes a miniature battery which generates a voltage based on the differential between the oxygen content of the exhaust gas and the oxygen content of the ambient air.
The voltage generated is usually about half a volt. But if the engine is running lean (too much air), then the exhaust gas oxygen content is closer to that of the ambient air and the voltage generated is less. If the engine is running rich (too much fuel), the exhaust oxygen content is much lower than that of the ambient air and the voltage generated will be higher.
With this information, the ECU can adjust the fuel/air mixture appropriately to keep it as close to ideal as possible. This can compensate to some degree for engine wear over time as well. The real benefit here is the ability to keep emissions of carbon monoxide, oxides of nitrogen, and unburned hydrocarbons as low as possible.