Like account and opportunity teams, case teams are meant to enhance the service process: define people that can have access to the case.

These people can be actual users or contacts, provided they are customer portal users.

The core of this kind of team is the case team roles configuration (Setup | Feature Settings | Service | Case Teams | Case Team Member Roles):

From here, you can define which role has which access level on the case team. You can set Private, Read Only, and Read/Write access levels. Visible in Customer Portal allows users from the customer portal to see that member.

From the case related list (you probably need to manually add this related list on the case page layout), you can select users you want to be part of your team:

The same sharing considerations apply for case teams as well.