Okay, leg weights are a pretty extreme method of taijutsu training. During the initial phases of training, the user will be equipped with very heavy leg weights that he must acclimate himself to wearing until they no longer hinder his movement. After a period of time has passed, the user has become quite used to them, and upon taking them off, they will be able to move freely and much much faster than they were capable before the training/when they are wearing the weights.
In addition to speed, the leg weight training also has the added benefit of adding power to the user's kicks, as the extra strength is obviously beneficial. I can also see benefits of having really really heavy kicks while the weights are on, but I'm not sure if that actually works. It seems like whenever Rock Lee kicked Naruto/Sasuke pre-chunin exam he should have broken bone on contact due to force, so maybe not? o-o