Why does passwd command show "UNIX password"?

It says UNIX because you're changing the password for authentication provided by the pam_unix PAM module. Quoting the manpage:

NAME
   pam_unix - Module for traditional password authentication

SYNOPSIS
   pam_unix.so [...]

DESCRIPTION
   This is the standard Unix authentication module. It uses standard calls
   from the system's libraries to retrieve and set account information as
   well as authentication. Usually this is obtained from the /etc/passwd
   and the /etc/shadow file as well if shadow is enabled.

It is related to Unix in that it uses the traditional files /etc/passwd and /etc/shadow as the source of authentication.

If you used another PAM module, like pam_ldap for LDAP authentication, it would say LDAP instead of UNIX:

$ passwd
(current) LDAP Password: 
New password: 
Retype new password: 
passwd: password updated successfully