Destroying barbarian huts is not only a great way to ensure that your suburb is protected, but also to get more prestige and goods!
 
The amount of prestige you are awarded will depend upon the difficulty of the barbarians.
 
The number of goods given as a reward for successfully defeating a barbarian is based on the number of goods that you can produce in your suburb per day.
 
Once the world progresses to higher Epochs, more goods will become available as rewards for defeating barbarians.