Your domestic league (English Premier League, Spanish La Liga, Italian Seria A, German Bundesliga, French Ligue A, etc) would be like your conference (SEC, Big 10, Pac 10, etc) but much more important. The Champions league would be like March Madness where the best teams from all the leagues, with the best leagues getting the most invites, play each other to determine the best European club. The UEFA Cup would be the NIT where the next best teams have their less prestigious tournament.