Overdrives were (yes, it's safe to say "were" here, only antiquated automatic slushboxes still have one) planetary gearsets that were found between the gearbox and transmission axle. It provided a direct link (off) or a surmultiplied link (on).
As a result you could get what normally now stands for a 5th gear. Some gearboxes even allows overdrives to work on other gears than the top gear, that could be very funny
Basically, overdrives are the past now. With one planetary gearset alone anyway you can have four gears AND reverse depending on the acting/reacting component, so...
Oh, and read this well: as the overdrive was after the gearbox it had to support the torque at the output of the gearbox, not the engine! That's sometimes confusing because for example the Haldex system brochure says it can stand up to 2500 Nm of torque... Well, yes, but that's 2500 Nm out of the gearbox. As a result, it couldn't be fitted to, say, a 330d because in first gear max torque out of the gearbox is more than 4000 Nm...