O/D is simply any gear with a drive ratio greater than 1:1
My god, I can't believe it took till post #13 to get this...
Overdrive is a gear ratio that results in the output shaft of the transmission spinning faster than the input shaft. That's it. It has nothing to do with torque converters. There can be more than one O/D gear in a trans: The 6-speed manual in a 2009 Corvette will actually have two overdrive gears; 5th gear is 0.71:1 while 6th is 0.57:1.
It's a highway gear. It's intended to reduce highway RPM to reduce fuel consumption and engine noise getting into the cabin. Your car feels slow in O/D because it is: With an O/D gear ratio, the torque at the output shaft of the transmission is actually
less that that at the crankshaft. Contrast this with 1st gear where you get a multiplication. The 4R70W has a 1st gear of 2.84:1, meaning the input shaft spins 2.84 times the output shaft speed and you see a 2.84 times torque multiplication. So if your engine makes 300ft-lbs at 4000RPM, you'd see 852 ft-lbs of torque (300*2.84) at the output shaft of the trans which would be spinning at just over 1400RPM (4000/2.84).
Now go into overdrive: At 4000RPM your engine still makes 300ft-lbs but the O/D gear ratio is 0.70:1, meaning you'd see just 210 ft-lbs (300*0.7) at the trans output though it'd be spinning at 5714RPM (4000/0.7). You can see the obvious here: You're going to be going quite fast but the car is going to feel very, very sluggish.
And what if the car goes into O/D in town when you're puttering along at 1200RPM, where the engine is making 80ft-lbs of torque? 80*0.7 = 56-ftlbs: You couldn't even tighten a lugnut with that. No wonder the car feels sluggish and slow with O/D on. Indeed, some of the world's most powerful cars top out at a lower speed in O/D simply because even they don't have the torque to overcome what the O/D takes away. They do better with a lower gear where the RPM climbs some but so too does the torque.
A "band" is simply a device in the transmission designed to control the rotation of a drum. If you've ever used a band-type oil filter wrench, you get the idea of a band in a transmission. When a band is active, a piston moves causing the band to tighten over its drum, stopping the drum from turning. Depending on what other components are driven -- all switched with clutches etc -- the output shaft can end up turning faster than the input shaft, giving an overdrive.