correct me if I am wrong

but my understanding is that the overdrive allows your car to switch from a higher gear from a lower one in order to generate more torque. For example, when you drive uphill on the highway, the OD may switch you from the highest gear to the next lower one to sustain a comparable speed. This, of course, means that the engine is running at a much higher RPM and becomes noisier. For local driving, having the OD on or off should not make much difference because even if you keep it one all the time, it is not going to kick in frequently.

I remember seeing this in a owner's manual for a friend's car. I doubt it differs by make/model.