It's common for people to stand with their knees straight, with their center of mass over the heels. When one is in this position, one can be collaquially "caught flat-footed", where one is slow to react because the the first motions required to move are to bend the legs and shift weight either towards the front or the side. In contrast, if one "stays on their toes", reactions are quicker because this preliminary motion is already completed.
This particular advice is in the context of standing qi gong, and not general fighting stances; it is more directly relevant to workers who stand most of the day standing than fighting concerns. If you stand for minutes with your legs straight and your weight over your heels, you will probably find this creates tension in your lower back and begins to cut off circulation to your feet. Moving the center of mass forward to the center of the foot is meant to align your body so that you need less muscular tension to stand. This has the caveat that if you retrain yourself to stand this way, you will probably need some weeks to adjust before you perceive benefits; you are likely in a local minimum and need to work to get to a more global minimum.
If you measure the pressure across your foot, standing with your center of mass over the center of the foot will approximately equalize pressure on the heel and ball of the foot. Standing with your center of mass over the heel increases pressure on the heels and reduces pressure on the ball of the foot.