In sport, if a tournament has for example 20 vacancies available, but there are 30 teams that want to play (too many teams), then the 30 teams play qualifying matches to determine which 20 teams will be allowed to enter the tournament.

Without the full context I'll make a guess. This is typically a sports related term and it's a game, a match, that qualifies (takes) the winning team into a competition, such as the World Cup for soccer (football).