Identity models for Office365

There are three identity models available for tenants using Office 365 (O365). Choosing one of the models will impact the way user accounts are managed and how users would log in to their Office 365 subscriptions.

The models available are:

1. Cloud identity model : All user accounts are store on the cloud in Azure Active Directory(AD). The Azure AD is the active directory used by O365 The tenant administrators could manage users through the O365 admin center.
2. Synchronized identity model: In this model the user identity is managed in an on-premises server and the accounts and password hashes are synchronized to the cloud. The user enters the same password on-premises as they do in the cloud, and at sign-in the password is verified by Azure AD. This model uses the Microsoft Azure Active Directory Sync Tool (DirSync). Link: http://go.microsoft.com/fwlink/p/?LinkID=510956
3. Federated identity model: This model also requires a synchronized identity, however the on-premise AD would validate the user credentials. This model uses ADFS or any other third party Identity provided supported by Microsoft. The identity providers supported are given here 

Reference:https://support.office.com/en-us/article/Understanding-Office-365-identity-and-Azure-Active-Directory-06a189e7-5ec6-4af2-94bf-a22ea225a7a9