Postural stability and control is an important factor when it comes to injury prevention and performance enhancement. Athletes will have to be able to stabilize, control, and maintain it. The better they are able to do it, the less risks of injury they will have and the better they will be able to perform no matter what the tasks and skills are. This is a main reason that a gymnast falls off from the beam, a figure skater doesn't land a triple jump, a soccer player hurts her knee, etc. To have a good postural stability, athletes will have to have enough strength, musce balance, proprioception, and they also need to be able to recruit muscles when they need to at a right timing. They will also have to have endurance to maintain it for a prolonged period of time. There are a lot different ways to achieve this and also depending on what their deficits may be, training methods will vary. But this is one of my favorite exercises to have an athlete do.
You stand on BOSU ball or something that challenges you to balance on and get in a squat position, holing a stretch exercise band attached to a wall at your shoulder height. Then, you extend the arms out as you maintain the good squat position without letting the BOSU ball tilt. Bring the arms back in towards your body and repeat. Also, keep in mind to maintain the neutral pelvic position.
Sounds easy?! Give it a try and find out!