A SAML service provider is a system entity that receives and accepts authentication assertions in conjunction with a single sign-on (SSO) profile of the Security Assertion Markup Language (SAML).
In the SAML domain model, a SAML relying party is any system entity that receives and accepts information from another system entity.
An important type of SAML authority is the SAML identity provider, a system entity that issues authentication assertions in conjunction with an SSO profile of SAML.
[OS 2] A relying party that consumes such assertions is called a SAML service provider (or simply service provider if the domain is understood).
Thus a SAML service provider is a system entity that receives and accepts an authentication assertion issued by a SAML identity provider.