Google OAuth 2.0 is Google's implementation of OAuth 2.0, the open standard for authorization, in which a user lets an app access data without giving the app a password. Google's OAuth 2.0 APIs serve both authorization and authentication; for sign-in they follow OpenID Connect, an identity layer on top of OAuth 2.0, and are OpenID Certified.
A developer first creates OAuth 2.0 client credentials in the Google API Console: a client ID, and for server apps a client secret, of a type that matches the app (web, Android, iOS, desktop, Chrome extension or TV). The app asks the Google Authorization Server for an access token with scopes, which limit what the token may do. Google shows the user a consent screen; if the user agrees, the app receives the token and sends it to a Google API in the HTTP Authorization header. A refresh token gets new access tokens when old ones expire. For sign-in the app receives an ID token, a signed record of who the user is.
Use is governed by Google's OAuth 2.0 Policies; the pages state no price.