I cam across this blog post (Geneva, Exchange Online) from the UC Three Amigos blog which has on of the best/simplest explanations of how Geneva works.
The extract below is ripped straight from their blog.
How does it work?
1. User clicks link for service
2. User taken to Microsoft Services Connector for authentication
3. Connector validates credentials with Active Directory
4. Microsoft Service Connector issues a login token and redirects to the Microsoft Federation Gateway
5. Gateway validates token and transform claims
6. Federation issues service token a directs to the service
7. user accesses the service.
This is exciting stuff for organisations looking to have spilt on-premise and cloud services as it is seamless to the user.