Run a file as root irrespective of who is running it.

It is a file permission, delegated as s allowing current user to execute that file as root. Yeah, kinda like a sudo

To set up setuid:

@: ls -l
-rw-r--r-- 1 niva niva 0 Dec 5 17:54

chmod u+s
@: ls -l
-rwSr--r-- 1 root root 0 Dec 5 17:54
Obeserve here the letter capital S. This means setuid is set, but the user that owns the file does not have execute permissions.
So, file to be executable by user do;
chmod u+x
-rwsr--r-- 1 root root 0 Dec 5 17:54