The term "tie-breaker" is used in tennis matches when the score reaches a tied situation, typically at 6-6 in a set. To determine the winner of the set, players engage in a tie-break game where the first player to reach 7 points (with at least a 2-point lead) wins the set. This mechanism adds excitement to matches and allows players to showcase their mental toughness and strategic skills under pressure, enhancing the competitive nature of the sport.