Leg Weights is essentially a method of training. It involves adding additional weights to ones legs so that normal movement will be more cumbersome. The idea behind this is that while the strain of the additional weight may initially make normal movement difficult, or maybe even impossible, once the body begins to adapt and once one becomes capable of moving as they normally would with the added weight on, they will be capable of moving even faster once they finally remove the weights.
It's basically systemic overload, increase burden to increase function.