All gearboxes work the same way: there is a gear on the motor, a
gear on the thing you're trying to drive, and sometimes a set of
gears between the two. The ratio between the gears, plus the RPM of
the motor, determines the speed of the workpiece. If the gear on
the motor is larger than the gear on the workpiece the RPM of the
workpiece will be higher than the speed of the motor. If the
workpiece's gear is larger, the workpiece will turn slower than the
motor. Given that, though, I've never seen a gearbox on a wood
lathe. Wood lathes use belt drive for two reasons, the most
important being safety--if you get a catch, a workpiece on a belt
driven lathe won't damage you as badly as a workpiece on a
gear-driven lathe. Also, belt drive won't feed vibration from the
workpiece back into the motor and damage the bearings. Gear drive
is used on metal lathes.