The term comes from SAML; in OIDC the same role is called relying party or client. The SP sends unauthenticated users to the IdP, receives the signed response, checks signature, audience and validity window, and then creates its own session.
For configuration the SP needs the IdP's metadata and publishes its own: entity ID, ACS URL and, if requests are signed, a certificate.
Many errors on the SP side come from the environment: behind a reverse proxy the SP builds wrong URLs, or the system clock drifts and valid assertions are rejected as expired.