VLSD stands for Viscous Limited Slip Differential.
In case you’re still none the wiser, a VLSD links the two wheels (in the case of the 350Z) using two sets of plates encased in fluid, all together in one sealed housing unit. When the wheel on one side loses grip, it spins faster, causing one of the sets of plates to spin faster. The liquid inside tries to catch up with the faster rotation of that set of plates, and in doing so transfers the torque to the slower set of plates. This effectively transfers the torque to the wheel that still has grip, so it spins up and the car gets moving.
There is a large drawback to this type of differential – after approximately 100,000 km, the fluid has all been used up and the differential is therefore acting in an open capacity, meaning that your differential is not actively controlling your wheels separately anymore. If one spins, so does the other. Once that happens, the VLSD needs to be replaced … oops!