The Set User ID (SUID) permission allows a file to execute with the privileges of the file owner, rather than the user who runs it. The /bin/passwdcommand is used by users to change their own passwords. The actual password hashes are stored in /etc/shadow, which is only writable by the root user. Since normal users do not have direct write permissions on /etc/shadow, the SUID bit on /bin/passwdenables the command to run with root privileges, allowing password changes.