Permissions
Usually, on most filesystems, deleting a file requires write permission on the parent directory (and execute permission, in order to enter the directory in the first place). (Note that, confusingly for beginners, permissions on the file itself are irrelevant. However, GNU rm asks for confirmation if a write-protected file is to be deleted, unless the -f option is used.)
To delete a directory (with rm -r), one must delete all of its contents recursively. This requires that one must have read and write and execute permission to that directory (if it's not empty) and all non-empty subdirectories recursively (if there are any). The read permissions are needed to list the contents of the directory in order to delete them. This sometimes leads to an odd situation where a non-empty directory cannot be deleted because one doesn't have write permission to it and so cannot delete its contents; but if the same directory were empty, one would be able to delete it.
If a file resides in a directory with the sticky bit set, then deleting the file requires one to be the owner of the file.
Read more about this topic: Rm (Unix)