Hmm. Typically, as folks have stated here, OD is just one more gear, with a ratio that makes the driveshaft spin faster than the engine, thus putting the engine in a lower rev-range, saving fuel and decreasing torque.
For around town driving, you can probably leave OD off as you might not ever reach this gear (like driving in 5th gear on a manual on local roads - you probably won't do it, maybe 4th at the most). There is no harm in leaving it on, assuming you are going to floor the car everywhere you go. If you are going to floor the car, and actually get to a point where you will continue to shift (like on a drag strip), you will want to leave OD off, as it is NOT a performance gear.
If you are cruising on the highway, by all means use OD - that's the point of it. If you are going to step on it to pass a car, you should be able to leave OD on, the car will just down shift.
Pressing the OD button doesn't necessarily mean something will happen right away. As stated, if you are cruising on the highway at like 70mph, and you push the button to turn it off, the car will act like you just downshifted a gear. That is all. If you are cruising on local roads in like 3rd at 30 mph or whatever, and you turn off OD, nothing will happen as you were not in the overdriven gear.