Developer Console is a Web console for developers to manage their client applications.
It is not explicitly written in any specification, but you have to provide third-party developers (and yourself) with a Web console for them to manage their client applications. It is a time-consuming task to develop such a tool, but you are free from the task. Authlete offers Developer Console and you can let your third-party developers use it.
To let third-party developers login Developer Console, you are required to implement a developer authentication callback endpoint. On the other hand, if you are the only developer for your service, you don't have to implement the endpoint. Read "Developer Authentication Callback" for details.
Anyway, this document describes how to use Developer Console.