From BR Bullpen
A quality start is a game in which the starting pitcher pitches six or more innings and allows three runs or fewer. The implication is that a quality start allows his team a much better than even chance to win the game and is a credit to the starting pitcher, whether he ends up with a win, a loss, or a no-decision for his efforts.
The quality start statistic is black and white: either a start qualifies, or it doesn't. Thus a pitcher who throws 5 2/3 scoreless innings and wins the game has not delivered a quality start, while his opponent, who gives up 3 runs over 6 innings and loses, has done so. Critics of the statistic often say that 6 innings with 3 runs represents a 4.50 ERA, and that this is not representative of quality. This may be true, depending on the offensive context, but it is also the extreme case; the average quality start is in fact much better than that.