In 20XX, mankind has left Earth and the once busy streets of Tokyo are now home to lions, tigers, chickens, and various other animals. All of them are now fighting for survival.
In Story Mode, the player plays through missions centered around various animals. Eventually, the player will discover the truth behind mankind's disappearance. A Pomeranian dog and thoroughbred racehorse are key characters in the story.
In Survival Mode, the player takes control of an animal and fights for survival against other animals for as long as possible. Tokyo Jungle has online leaderboards so the players can compare their survival skills against one another. Smaller animals will fight in groups, and the player's group can win fights against larger animals by just having at least one member of the group still standing.
Source: Wikipedia, "Tokyo Jungle", available under the CC-BY-SA License.