While the Volt does have a gearbox, it doesn't really have gears -- at least, not in the way a typical car does. If you're interested, go read this article to get an overview of all the bizarre things that the Volt is actually doing under the hood, it's quite ingenious.
However, from a practical standpoint, the only difference between Drive and Low "gear" on the Volt is in how the onboard computer interprets the desires of the meatbag it is hauling around town.
The basic difference between the two modes is what happens when you take your foot off the gas. When in Drive, it pretends to be just like a normal car -- the Volt will coast and very slowly decelerate, and you use the brake pedal to come to a stop. Light brake application engages regenerative braking mode, where the electric motor acts as a generator, converts some of the kinetic energy of the car back in to electricity, and stuffs it back into the battery. Step harder on the brakes, and the regular disc brakes engage, and all that lovely Ke gets turned into heat.
"Drive" is the Volt's training wheels. To really feel like you're in an electric car, shift to Low. Now as soon as you take your foot off the gas, the Volt goes into smooth regenerative braking. It feels like a parachute just popped out of the trunk, and is very different from a normal car. It takes a little getting used to -- I've only had the car for a few days, and I'm still getting the knack -- but it lets you do these silky smooth approaches to stop signs and turns; you'll only touch the brake pedal right at the very end.
Chevy recommends Low for stop-and-go city driving, and Drive for highway, but the general consensus is that you can stay in Low whenever you're just using the battery.
If you decide to test drive a Volt, do half the drive in Drive, and the rest in Low. It's really a notable difference.
PS: I'm told that in Low mode, the brake lights don't go on until you actually touch the brake pedal. There is some concern this may confuse unwary tailgaters. Perhaps Chevy should consider a software upgrade that flashes the brake lights every couple of seconds when regeneratively braking.