Internet2's Shibboleth project aims to support inter-domain web resource sharing. It actually represents three separate developments:
a set of architectures and policies within which this sharing can take place
a set of profiles of the Security Assertion Markup Language to support this
an example open-source implementation
There is at least one other Shibboleth implementation: Guanxi from the UK's University of the Highlands and Islands
Shibboleth relies on the Security Assertion Markup Language (SAML), an XML dialect for exchanging authentication and authorisation data [authentication - the process of proving who you are; authorisation - the process of working out if you can do what you are trying to do]