I've seen a couple videos and there is a slight increase in sprint speed. May I ask how they affect the other movements? Do they move faster or something?

Really? I've never noticed noticed a difference and always heard otherwise. That could very well be true, though. It increases your general movement speed, like strafing, moving while aiming, etc.. It makes you generally harder to catch, which is important when you run low armor and recovery, like most Hunters do.