Shibboleth implements Federated Authentication, in which one organisation chooses to trust an authentication decision made by someone else.
This sort of authentication should make life easier for users since it uses something that they (should) already know, rather than a new user name and password. It also saves the SP from having to issue and manage its own authentication credentials.
Shibboleth (currently) rather assumes people only have a single home organisation – you can use more than one, but only one at a time. This may eventually be problem for people with multiple affiliations who want to take advantage of all their entitlements simultaneously.