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Portable Operating System Interface for Unix (POSIX) permissions are standards that dictate how Unix-based operating systems should function. POSIX permissions are how OS X refers to its legacy file permissions that allow OS X to be part of the Unix family of operating systems. As mentioned, the last three items listed in the Edit Permissions screen are the POSIX permissions. These include an Owner, a Group, and Everyone. The owner can be any user on the system, the group can be any group on the system, and Everyone includes all authenticated users.
The permissions for Owner, Group, and Everyone are set using the drop-down menus next to each entry in the Finder Info screen. The settings for each are: