The group of the partition is the means by which file/directory sharing will be done. Read access allows anyone in the group to read the files/directories in the top level of the partition, subject to their individual protections as well. Write access allows anyone in the group to add/rename/delete files/directories in the top level. Typically, this will be a file sharing or login group associated with the project. (Consult a list of groups used on the DCS faculty machine or one for the DCS research machine for possibilities.)

Protections for world mean the same thing as group definitions above for everyone not either the owner or in the group. This is normally just read access unless you're really worried about other users seeing the names of the directories in your partition. (Remember, access to the directories and files therein is controlled by their own protections.)

The two basic protection modes would be read/write and read only for group. Read/write allows users in the group to create their own directories. Read only is a more controlled approach, requiring coordination with the owner. If a group member requires a top level directory, the owner could set the group write bit for the partition, have the group member create the directory, then clear the bit.

For more information, see my page on sharing a directory.