A Service Provider (SP) is a key part of the SAML specification.
The Service Provider is the website or application which the user wishes to connect to. The Service Provider has an existing trust setup with the IdP (Identity Provider) and typically forwards the user to the IdP with a SAML message when a login is required.
Once the user logs in to the IdP they are redirected back to the Service Provider. The Service Provider then consumes the response and decrypts the SAML message. The details of the message, including attributes, are then consumed by the website or application.
At this point it is expected behaviour that the Single Sign-on process will proceed. There are various settings which each Service Provider may adopt, such as auto-user provisioning (that means, creating a new user on first login), or updating the users data from the attributes returned from the IdP.