Leading a target means aim just a little ahead of the target. If the target is running to the right, you'll want to aim bit further to the right of him. Leading allows for the shooter to make up for the bullets' trajectory, because once the bullet leave the barrel of the gun, it will stay on a linear path, or a straight line. Because the target is moving, and the person aims where the target is at that point in time, they might miss the target, provided they are traveling at a fast enough speed, or are a required distance away.
This wasn't needed in the first game because the first game had bullets travel instantaneously, this is basic adding vectors, it'll make sense if you think about it that way.