An IdP is an authoritative source of identity information for users affiliated with the organisation running the IdP. Relying Parties will have a trust relationship of some kind with the IdP that means they trust it to authenticate and authorise users.
The client interacts directly with the IdP through a secure tunnel that passes through the Service and its RP Proxy. The user proves who they are to the IdP through this tunnel via a credential exchange of some kind (e.g., passing a username and password across).
Once the user has successfully authenticated to the IdP, the IdP in turn responds to the Service via its RP proxy; it may provide information solely to acknowledge that a user authenticated correctly, or it may provide further information in the form of attributes such as name or membership information.