Like VCheng said, overdrive is basically a gear ratio lower than 1:1- when the engine is turning slower than the transmission. In mos cars, it's basically 5th gear. I'll give you an example:
Our Camry has an overdrive, which is basically 5th gear. It also has that infamous "O/D Off" switch that comes in most Toyota's, which basically kicks the gear down into 4th (1:1). That switch basically has a gear "connected" to it, and when you press it, it kicks down.
My Mazda on the other hand doesn't have an overdrive. It's a 4 speed auto, but 4th gear has a ratio of, I think, 0.8:1. But that's not really called an overdrive... it's just 4th gear.
A friend of mine has an old '70s Volvo 1800ES with a 4 speed manual and an overdrive option which is a switch, and you press it to engage a 0.79:1 gear.
So... that's my mindless rant.