Sign in with Microsoft is the sign-in button that apps show for the Microsoft identity platform, Microsoft's cloud identity service. Users sign in to a third-party app with a Microsoft account they already have: a personal account, as used for Outlook.com, Xbox and Skype, or a work or school account managed in Microsoft Entra ID.
The platform is an authentication service built on OAuth 2.0 and OpenID Connect, open standards in which an app sends the user to the identity provider's sign-in page and receives signed tokens that say who the user is and what the app may access. A developer registers the app in the Microsoft Entra admin center and uses the open-source Microsoft Authentication Library (MSAL), or another standards-compliant library, which runs the token flows and caches the tokens. The same tokens can authorize calls to Microsoft APIs such as Microsoft Graph. Microsoft provides official button images and branding rules for the Sign in with Microsoft button.
It is a hosted service. For apps that serve consumers or business customers, Microsoft Entra External ID bills by monthly active users and has a free tier.