Public Groups consist of a set of users. A group can contain individual users, other groups, or the users in a particular role. It can also contain the users in a particular role plus all the users below that role in the hierarchy.
Public groups can be used when defining sharing rules thus limiting the multiplication of the latter . They are also used to share or release information (access to a reports folder, sending emails …).
Beware, they have the same name as the public groups in Chatter, but nothing to do with!
Each user can see in his personal settings which public groups he belongs to.