Windows Server ADFS Design and Authentication Process

AD FS is a standards-based service that allows the secure sharing of identity information between trusted business partners (known as a federation) across an extranet. When a user needs to access a Web application from one of its federation partners, the user’s own organization is responsible for authenticating the user and providing identity information in the form of “claims” to the partner that hosts the Web application. The hosting partner uses its trust policy to map the incoming claims to claims that are understood by its Web application, which uses the claims to make authorization decisions

Following diagram shows high level steps how the claim base authentication works.