Federated identity services allow organizations to extend their on-premise user directories to cloud services, enabling single sign-on (SSO) and centralized management of user identities and permissions across heterogeneous environments. This is crucial for hybrid cloud setups that need to manage identities across on-premise systems and cloud services without duplicating identity stores.

'Cloud-only identity services' would not utilize the existing on-premise Active Directory, which does not support the scenario's requirement for integration. 'On-premise synchronization without any cloud integration' misses the need for cloud services integration and would not support a hybrid model. 'Multi-factor authentication' adds a layer of security but does not address the seamless integration of identity management between on-premise and cloud systems.