The myth of core stability is popular for one reason; its visual association with chiseled abs and a thin waistline. In fact, foot stability is significantly more important, but not many people would prefer a better looking foot to six pack abs. Part of the reason your foot isn’t sexy is the large number of structures jammed into a very small space. The human foot and ankle contains 26 bones, 33 joints, and more than a hundred muscles, tendons, and ligaments. With all of those pieces, there has to have been some stimulus or need for such intricacy. Since your ground reaction force (GRF) is the most important characteristic, it would make perfect sense that the most necessary stability comes from the first interaction with the earth, which is the foot.
Stability is your ability to resist movement, especially at the end ranges of motion. One of the best ways to enhance foot stability, or any movement that challenges your balance, is to increase the surface area. The more area in contact with the ground, the easier it is to move quickly or resist movement. Perhaps the easiest example is how much more stable you are standing on two feet versus one. For those of you who have had too many concussions, you have half the surface area when on just one foot.
We mentioned stability being exposed at end ranges of motion, and a great example occurs when you are jumping and have to finish off your toes to move in the desired direction. If the foot is unstable, that toe off period is shortened or directed in a less desirable direction.
The best way to improve your stability is to provide movements that just take longer for each rep such as heavy, single leg movements (lunges, split squats, etc.). Loaded carries like sled pulls/resisted march require you to move in different directions than vertical.