Pretty straightforward: o/d off is 3rd gear, o/d on is 4th (top) gear, which allows you to run the car at a lower rpm compared to 3rd gear at the same speed, which gives you better fuel economy (especially on highways). You should turn o/d off (switch down to 3rd gear) only when you need more acceleration/torque in situations such as passing, going uphill, or towing something. Same can be achieved by just flooring the throttle, telling the car's computer that you need to accelerate faster so it'll downshift to 3rd for you. But some people (like me for instance) wouldn't like to wait til the computer shift for me, so pushing the button downshifts to 3rd almost instantly, but remember to push the o/d button again to turn it back on when you're done passing or going uphill.
And yes, since today's Toyota's o/d button is a one-state button (unlike 2-states button of the past which stays down after you pushed it, and will revert to up position if you press it again), only the dash o/d off light (and perhaps by feel and sound of the drivetrain) will tell you whether you have o/d on or off. So everytime you turn off the car and crank it back on again, o/d is on by default.
Hope this help, and really, go ahead and try out the o/d button when it's safe to do so. Trust me, you won't break anything. Otherwise you might be better off with a manual