From Wikipedia:
The objective of the console games is to go to each of nine Districts and build their reputation (called "Rep", in-game). Rep is a measure of how popular a character is; as a character gains more reputation, they gain access to larger apartments and different Districts. In the end, the character will have the largest apartment and be able to visit any of the Districts.
In addition to gaining Rep, the player must also make sure that his or her character has its needs fulfilled, and to increase the character's skills by playing mini-games. The amount of money Sims can make at the various jobs in each of the districts is determined by what skills they've leveled up. As they progress through the game, players will get messages for rent from Darius, the Sim with the highest rep in the city, and get programmed messages to their XAM. Also, other challenges, like helping Sims (or Urbz) get money from people, or taking pictures of Urbz.
The player will be given different tasks depending on the District they're in. The tasks are varied in nature, including fulfilling needs, furnishing an apartment, building reputation, mastering a job, making friends, tagging an object, and helping others.