I believe that mower has a differential, not a single wheel drive. It works in the same way as the differential in a car: it drives both wheels with equal torque at all times, while allowing the two wheels to roll at different speeds. The "lock" simple disables the differential and locks the two wheels together, so one of them has to skid for the mower to change direction. The reason to have the lock, is that when the differential is working, if one wheel is on low-traction ground (such as slimy mud) it will slip, and because both wheels are driven with the same torque, that means there will be hardly any drive to the wheel that is not in the mud, and the machine won't go anywhere. Farm tractors always have a diff lock accessible from the driving seat - sometimes with a pedal as well as the lock lever, so you can just step on the pedal for a moment when a wheel starts to slip, and release it when you are through the soft spot.
