Using Plastic a developer can have a clone of the repository on his local machine and checkin, branch and merge without connection to the main server. This is what fully distributed is about.
The benefit is clear in terms of speed, enabling developers to work from home without suffering slow VPNs or being hit by a network issue. Developers can pull and push changes to any other Plastic server (depending on the permissions) anytime. In extreme distributed environments, developers wouldn't even use a central server. However, in practice, a central place will be used as rendezvous point.