It multiplies the last gear... somehow, so it's higher. It's like having another gear, but cheaper. Pretty common on automatics.
My Delta 88 (and many GM cars, in my experience) has another position on the shifter instead of a switch like this (so there's Drive (overdrive allowed) and Drive (no overdrive)).
I loved that switch on my Supra, when you turned overdrive off, the engine would be right at the start of the powerband at 60 km/h. Just a little nudge on the gas pedal and the car would take off. Pretty fun, because the engine wasn't in great shape and it was an automatic, so that's about the only time it was fast.
The really cool way to do it (this doesn't) is if the overdrive unit is an independant thing that multiplies the gear ratio, it can make a 4-speed into an 8-speed! Sort of. Since you've only got 4 real gears and one multiplier, the gears can't be as useful as if you had 8 real gears.
This is sort of how semi trucks/tractors/prime movers/lorries/whatever have 18 gears. Instead of just overdrive on/off, there's a whole additional transmission (I think it's actually just a really tricky multiratio differential. Same effect though). Like having a 12/18/21 speed bike, 2 or 3 gears on the crank and 6 or 7 on the cone.