The umask acts as a set of permissions that applications cannot set on files. It's a file mode creation mask for processes and cannot be set for directories itself. Most applications would not create files with execute permissions set, so they would have a default of 666, which is then modified by the umask.
As you have set the umask to remove the read/write bits for the owner and the read bits for others, a default such as 777 in applications would result in the file permissions being 133. This would mean that you (and others) could execute the file, and others would be able to write to it.
If you want to make files not be read/write/execute by anyone but the owner, you should use a umask like 077 to turn off those permissions for the group & others.
In contrast, a umask of 000 will make newly created directories readable, writable and descendible for everyone (the permissions will be 777). Such a umask is highly insecure and you should never set the umask to 000.
The default umask on Ubuntu was 022 which means that newly created files are readable by everyone, but only writable by the owner:
user@computer:~$ touch new-file-name
user@computer:~$ ls -dl new-file-name
-rw-r--r-- 1 user user 0 Apr 1 19:15 new-file-name
Starting in Ubuntu Oneiric (11.10) the default umask was relaxed to 002, which expands write-access to the owner's group:
user@computer:~$ touch new-file-name
user@computer:~$ ls -dl new-file-name
-rw-rw-r-- 1 user user 0 Apr 1 19:15 new-file-name
Viewing and modifying umask
To view your current umask setting, open a terminal and run the command:
umask
To change the umask setting of the current shell to something else, say 077, run:
umask 077
To test whether this setting works or not, you can create a new file (file permissions of an existing file won't be affected) and show information about the file, run:
user@computer:~$ touch new-file-name
user@computer:~$ ls -dl new-file-name
-rw------- 1 user user 0 Apr 1 19:14 new-file-name
The umask setting is inherited by processes started from the same shell. For example, start the text editor GEdit by executing gedit in the terminal and save a file using gedit. You'll notice that the newly created file is affected by the same umask setting as in the terminal.
Use case: multi-user system
If you are on a system that's shared by multiple users, it's desired that others cannot read files in your home directory. For that, a umask is very useful. Edit ~/.profile and add a new line with:
umask 007
You need to re-login for this umask change in ~/.profile to take effect. Next, you need to change existing file permissions of files in your home directory by removing the read, write and execute bit for the world. Open a terminal and execute:
chmod -R o-rwx ~
If you want this umask setting be applied to all users on the system, you could edit the system-wide profile file at /etc/profile.
Best Answer
The 027 umask setting means that the owning group would be allowed to read the newly-created files as well. This moves the permission granting model a little further from dealing with permission bits and bases it on group ownership.
This will create directories with permission 750.
Please check this great article 027 umask — a compromise between security and simplicity.