REPU is a semi-decentralized non-transferable token intended to be used as a reputation system on Edgeware. The REPU token can only be issued and burned by trusted entities that follow the agreed upon standards (hence the term semi-decentralized).
A reputation token like REPU has many use cases in community governed chains and blockchain communities in general. For forums and governance platforms like Commonwealth it can be used to reward users who contribute to the growth of the community as well as a means to moderate and prevent trolling. Reputation in chain based P2P lending platforms allows lenders to mitigate risk by giving them a measure of "trustworthiness".
The token has a controlling owner which ideally should be a democratically elected council such as the Edgeware Council. This owner is able to add entities and has number of other privileges. A system where there is no controlling owner is also possible. For example, the contract could require that 75% of the admins agree to adopt a new standard instead of the owner adding it.