The player controls one of five animals (they can choose between cow, pig, bat, rat, and penguin) and plays games against all the other animals. In the Nintendo Entertainment System and arcade editions of the game the five animals are penguin, bear, panda, shimmying koala and beaver. In each game, the participating animals find each other on opposite sides of a square table with five balls on each side. The object of the game is to roll those balls over the table. As soon as all ten balls are on one player's side, that player loses the game. Each game also has a time limit of 60 seconds; if that is reached, the player with the fewest balls on their side wins.
If a player is hit by one of the balls, they are knocked unconscious for a certain amount of time. Thus, it could also be said that part of the object of the game is to hit the opponent, as otherwise it would not be possible to get all ten balls to the other side (the opponent can just roll them back before all of them have arrived).
The different animals have different strengths and weaknesses which are a trade-off with each other. For example, the rat is the one that can move left and right the fastest, but in return he can roll the balls only very slowly. The cow, on the other hand, is a very slow walker, but in return she regains consciousness quicker.
After 30 seconds of playing, a jellybean-like obstacle appears in the middle of the table which moves left and right. Different kinds of these obstacles cause varying effects on the trajectory of the balls; some deflect them so they start rolling diagonally (the players themselves can only roll them parallel to the sides of the table), whereas others simply have the ball bounce straight back.
Source: Wikipedia, "Penguin Wars", available under the CC-BY-SA License.