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AuthnQuery (v2)
<AuthnQuery xmlns="urn:oasis:names:tc:SAML:2.0:protocol"
                       ID="abe567de6"
                       Version="2.0"
                       IssueInstant="2005-01-31T11:58:00Z"
                       Destination="https://www.AirlineInc.com"
                       SessionIndex=310">
    <Subject xmlns="urn:oasis:names:tc:SAML:2.0:assertion">
        <NameID Format="urn:oasis:names:tc:1.1:nameid-format:emailAddress">
            j.doe@acompany.com
        </NameID>
    </Subject>
</AuthnQuery>
see example09.b
"Hey IdP, give me all the assertions that you have which contain authentication statement(s) which match this subject and which match this session index."
When a user interacts with an IdP, that is called a session. Typically, an IdP will associate a number with the session.  That number is called a session index.