Worldwide mode it's one of the three modes available on Online Multiplayer. There you have two options to play against another players: race or battle.
Like Mario Kart Wii, Mario Kart 7 has the Race mode, where a single player has to compete against worldwide opponents in order to obtain VR. The Race mode has three engine classes, 50cc, 100cc, and 150cc (they're selected in order). The higher the engine class, the harder the races will be against the opponents. If all players complete all the engine classes available on Grand Prix, they can race on Mirror class.
In Battle Mode, the player can select one of the two types of battles available in Mario Kart 7 and one of the six battle courses that appear in this mode. 3 of the six battle courses are new, and the remaining 3 battle courses are from previous installments in the series.
Racers compete each other by popping the opponent’s balloons to gain points in a time limit of two minutes. All racers start with three balloons and must use the items from the Item Boxes to take away a balloon from their opponents. Hitting a rival is worth a point. If the racer has one balloon remaining and is hit, half of the player's points will be taken out and the player will be momentarily out of the battle to respawn with three balloons again and continue to play.
In Coin Runners (Coin Battle in Europe), racers collect the Coins spread in the battle course within the time limit of two minutes. The racer that has the most Coins at the end wins. Racers can use the items to hit the opponents and make them drop a maximum of 3 coins of the coins they have collected. As with Grand Prix and Time Trials, only 10 coins can be held onto at once. Coins collected in this mode do not count toward the coin total to unlock kart parts.