A referee's discretion is pivotal in situations where rules are ambiguous or subjective, such as when determining fouls, penalties, or interpreting the intent behind a player's action. This judgment can greatly influence the game's dynamics, as referees must assess the seriousness of an infraction and make quick decisions. Their discretion helps maintain the game’s flow while ensuring that players adhere to the spirit of the rules, which can lead to tense moments during critical phases of the competition.