The profit-maximizing quantity of labor refers to the number of workers that a firm hires to maximize its profits, where the marginal revenue product of labor equals the marginal cost of hiring additional workers. In monopsony markets, this concept is crucial because there is only one buyer of labor, giving the employer more control over wage setting and employment levels. Firms in a monopsony can influence wages by adjusting the quantity of labor they demand, leading to different hiring decisions compared to competitive labor markets.