Network security basically attempts to answer two questions: "who are you?" and "should you be doing that?" Authentication proves who you are. Authorization defines what you're allowed to do. Typically the way a server decides whether someone should have access to a resource is by first authenticating the user, and then consulting a database associated with the resource that indicates who is allowed to do what with that resource. For instance, the database associated with a file might say that Alice can read it and Bob and Carol can both read and write it. This database is often referred to as an ACL (access control list).
Another model of authorization is known as the capability model. Instead of listing, with each resource, the set of authorized users and their rights (e.g., read, write, execute), you would have a database that listed, for each user, everything she was allowed to do.
If there were only a single resource, then the ACL model and the capability model would be basically the same, since in both cases there would be a database that lists all the authorized users and what rights each has to that resource. But in a world in which there are many resources, not all under control of one organization, it would be difficult to have a central database listing what each user was allowed to do (for instance, all the files that user is allowed to read), and it would have scaling problems if there were many resources each user was allowed to access.
Some people worry that ACLs don't scale well if there are many users allowed access to each resource. But the concept of a group answers that concern. A very basic form of group implemented in some systems is that each user is a member of one group, and someone with special privileges assigns users to groups. There is a special group known as "world", which includes everyone. Alice would be allowed to read a file if her name was listed on the ACL with read access, or if her group was listed on the ACL with read access, or if "world" was given read access.
Extensions to the idea of groups that might be useful:
allow a user to be in multiple groups (researchers, security experts, U.S. citizens)
allow anyone (not just someone with special privileges) to create a group. Allow anyone to name that group on an ACL they are authorized to administer.
allow a group for which the user explicitly invokes his membership. This type of group is known as a role. The main difference between what people think of as a role and what people think of as a group is that the user always has all the rights of all the groups he is a member of, but only has the rights of the role he has explicitly invoked. Some people would claim that if the user is allowed to assert multiple roles, he can have only one of them active at any time.
We discuss ways of implementing very flexible notions of groups in §15.8.3 Groups.