Bocce is similiar to soccer. In soccer the most important object of the game is to get the ball into the goal of the opposing team more often than they do, within an allotted time period. In bocce the most important object is for one or more of your teams balls to be closer than any of your opponents balls to the pallina (small target ball, often white) at the end of every set. You can play by time, or by reaching a predetermined total score.
There are other governing rules and nuances which makes the difference between just fun play up to international competition, but the main goal is always the same as above.