Federation means that you can subscribe from one server to the activity/news etc. feed of any other user on a different, compatible server (i.e. another StatusNet server like identi.ca). This is similar to the way emails are sent from one provider to another.
To address somebody on a different server use the pattern @firstname.lastname@example.org (i.e. @email@example.com).
To post to a federated group you have to become a member of this group, afterwards you can send notices to the group just by using !groupname. To post to a remote group you have to use its original groupname, aliases for the group name are not federated at the moment (bug 3092).
Sending direct notices between users of different StatusNet servers does not work yet. Also sending private notices does not work federated.