Flow: the application (SP) redirects the browser to the IdP, the user signs in there, and the IdP posts a signed SAML assertion back through the browser to the application's Assertion Consumer Service (ACS) URL. It contains the NameID and attributes such as email or groups.
Both sides exchange metadata: entity ID, endpoints and the signing certificate. SAML is widespread in enterprise environments; Nextcloud supports it via the user_saml app.
Common errors: an IdP certificate that expired or was rotated without updating the SP, an entity ID that does not match exactly, clock skew beyond the allowed tolerance, and an ACS URL with http instead of https behind a reverse proxy.
Example
https://cloud.example.com/apps/user_saml/saml/metadata