What does the oxygen sensor do on a car?

It is the primary measurement device for the fuel control computer in your car to know if the fuel-air mixture is too rich or too lean. The O2 sensor is active anytime it is hot enough, but the computer only uses this information in the closed loop mode. Closed loop is the operating mode where all engine control sensors including the oxygen sensor are used to get the optimum fuel economy, with lowest emissions and good power.