A backbone network is normally independent of the internet and used for traffic between your servers that you do not want either slowed down by the internet traffic or to slow down the internet traffic its self. Lets say you have 4 servers (two load balanced web servers with their own database servers. The reasons to set up a backbone would be:
1. You don't want to be charged for the traffic between your systems as part of your bandwidth.
2. You want the web servers to talk to the database servers without web requests interferring.
3. You want the database servers to replicate data back and forth without web traffic interference.
4. You would not even have to have the database servers on the internet which would make them more secure.
Another main use for the backbone is it sends traffic between networks and large subnets. So from the server farm to client machines, or one building to another building. If you lookup some cisco ideologies and designs, its the core network. It will have high bandwidth links and fast devices to send the traffic