Composure can help predict how someone is going to respond in a crisis kind of situation. Will the person remain calm, collected and in control? While they hit the panic button? It is that ability to put a bad play behind and move on. It is that that ability to remain focused after the referee makes a bad call or a teammate makes a mistake.
For an athlete, it's important to be composed because this avoids ups and downs throughout the season. For the coach, is important to know the athletes composure so that the coach does not put the athlete in a compromising position, the wrong situation.