Bill the user: "Hey Jimmy, show me that report"
Jimmy the SP: "Hey, I'm not sure who you are yet. We have a process here so you go get yourself verified with Bob the IdP first. I trust him."
Bob the IdP: "I see Jimmy sent you here. Please give me your credentials."
Bill the user: "Hi I'm Bill. Here are my credentials."
Bob the IdP: "Hi Bill. Looks like you check out."
Bob the IdP: "Hey Jimmy. This guy Bill checks out and here's some additional information about him. You do whatever you want from here."
Jimmy the SP: "Ok cool. Looks like Bill is also in our list of known guests. I'll let Bill in."
Bill the user: "Hey Bob. I want to go to Jimmy's place. Security is tight over there."
Bob the IdP: "Hey Jimmy. I trust Bill. He checks out and here's some additional information about him. You do whatever you want from here."
Jimmy the SP: "Ok cool. Looks like Bill is also in our list of known guests. I'll let Bill in."
I go into more detail here, but still keeping things simple: https://jorgecolonconsulting.com/saml-sso-in-simple-terms/.