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All overdrive means that the (engine crankshaft to drive shaft) gear ratio is less than 1 to 1.
In other words, the drive shaft is spinning faster than the crankshaft.
This is mainly useful to reduce rpms and improve fuel economy.
So, basically it is another gear.
As to why there is a separate button for it, I don't know.
Well you can still accelerate when in overdrive, but it'll be much slower.
But yes, you want to be in overdrive on the highway if you reasonably stay within the same speed.
My friends dad has an overdrive on an old land rover series 3, he can do 40 in reverse with it. Trust me, 40 in reverse in an old landrover is seriously scary!