Unix File Permission – Meaning of the First Digit in 4-Digit Octal Notation

From man chmod:

A numeric mode is from one to four octal digits (0-7), derived by adding up the bits with values 4, 2, and 1. Any omitted digits are assumed to be leading zeros. The first digit selects the set user ID (4) and set group ID (2) and sticky (1) attributes.

What are "set user ID", "set group ID", and "sticky", you ask?

setuid/setgid:

setuid and setgid (short for "set user ID upon execution" and "set group ID upon execution", respectively) are Unix access rights flags that allow users to run an executable with the permissions of the executable's owner or group. They are often used to allow users on a computer system to run programs with temporarily elevated privileges in order to perform a specific task. While the assumed user id or group id privileges provided are not always elevated, at a minimum they are specific.

Also, when applied to a directory, the setuid/setgid cause new files created in the directory to inherit the uid or gid, respectively, of the parent directory. This behavior varies based upon the flavor of unix. For example, linux honors the setgid, but ignores the setuid on directories.

And sticky:

The most common use of the sticky bit today is on directories. When the sticky bit is set, only the item's owner, the directory's owner, or the superuser can rename or delete files. Without the sticky bit set, any user with write and execute permissions for the directory can rename or delete contained files, regardless of owner. Typically this is set on the /tmp directory to prevent ordinary users from deleting or moving other users' files.