Overdrive is for extra fuel economy, but makes climbing hills harder.
If the vehicle is unloaded, or lightly loaded, if the road is level or only slightly sloped, you want overdrive on to save fuel.
On the other hand, when fully loaded, or climbing a hill, or running into a stiff headwind, cutting off the overdrive will give you more power at the expense of higher fuel usage.
Overdrive is a higher gear ratio, and lets the engine run slower. When the load is heavy and power is needed, the lower gear ratio of overdrive-off allows the engine to rev higher and gives it more leverage/mechanical advantage.
Most vehicles with such a button can be (and should be) driven most of the time with overdrive on.
