The mkdir command is used to make a directory. In this example, the "foo" directory is created.
The ls (list) command with the -l (long) option can be used to view the standard permissions and ownership of the newly created directory. By default, the standard permissions of a newly created directory will be drwxr-xr-x. The "d" indicates it is a directory. Additionally, the directory will be owned by the user that created the directory (root in this example).
ls -l /tmp . . . drwxr-xr-x 1 root root 4096 Sep 18 19:02 foo
Permission denied will be displayed if you do not have write permission to the parent directory. For example, let's say you want to create a directory under /opt. In this example, only root has write permission to the /opt directory. In other words, only root will be able to create a directory under /opt. All other users will get permission denied.
This can be resolved by giving sudo permission to the mkdir command.
ls -ld /opt . . . drwxr-xr-x 1 root root 4096 Sep 18 13:49