This is a baseball phrase applied subjectively to an at-bat the speaker believes went well and had a good result. It can refer to a pitcher's or batter's performance, but most often it is the latter. In the case of the former, an individual would be referring to the fact that a pitcher pitched well, to the right spots, and did not over exert themselves or throw more pitches than necessary to get the batter out. In the more common case, a quality at bat would entail an at-bat in which the batter works the pitch count and gets the pitcher throwing lots of pitches and possibly tiring them out. It may or may not result in a hit or a base on balls.
The phrase is extremely subjective and cannot be quantified. It is most often used by fans and broadcasters speaking about the game. It is also used as a compliment from players and coaches to a batter who strikes out but did very well getting the pitcher to throw a lot of pitches. An example of its usage in that case would be, "Billy really had a quality at bat, he made him throw 12 pitches!"