(excerpt from http://gloriouskrishna.blogspot.com/2011/11/taraka-brahma-nama-holy-name-which.html)

Taraka Brahma Nama (The Holy Name which Delivers All) ‘taraka-brahma-nama’ which means this transcendental mantra is the deliverer of one and all.

narayana para veda narayana paraksara narayana para muktir narayana-para gatih

The purport behind it is -- Narayana is the abode of all vijnana, mukti (liberation), and the ultimate goal. This is aisvarya-gatah-nama; it is aisvarya, not madhurya, it is all opulence. Narayana is aisvarya-gatah-nama-narayana. Krsna-nama is madhurya, which is only available in the Kali-yuga.

rama narayanananta mukunda madhusudana krsna kesava kamsare hare vaikuntha vamana

What is the purport in it? The taraka-brahma-nama in the Satya-yuga only gives santa and dasya-bhava. No other bhava, mellow, only santa and dasya. But in the Treta-yuga, the taraka-brahma-nama gives dasya (servitorship) and some glimpse of friendship, sakhya-bhava -- sakhya-nama. This Treta-yuga taraka-brahma-nama is also aisvarya gatah, all the names of Narayana are there and here it is said, multifarious -- vikrama, Lord Vamana -- trivikrama. Lord Vamana exhibited three types of vikrama, He manifested three wonderful potencies, known as trivikrama -- Vamana.

hare murare madhu-kaitabhare gopala govinda mukunda saure yajnesa narayana krsna visnos nirasrayam mam jagadisa raksa

Here you will find santa, dasya, sakhya and vatsalya -- these four mellows, and nirasrayam mam jagadisa raksa. Taking complete shelter at the lotus feet of Jagadisa, the Supreme Lord of the Universe, and no other shelter.

hare krsna hare krsna krsna krsna hare hare hare rama hare rama rama rama hare hare

This is madhurya, it is the best of all, it has such great potential and it is so powerful. It is madhurya, there is no aisvarya at all. In all the names in the other yugas you will find there is aisvarya, but here in the Kali-yuga -- hari-nama: Hare Krsna Hare Krsna Krsna Krsna Hare Hare, Hare Rama Hare Rama Rama Rama Hare Hare; this is completely madhurya-nama, all the mellows are there. Thus Mahaprabhu chanted this: Hare Krsna Hare Krsna Krsna Krsna Hare Hare, Hare Rama Hare Rama Rama Rama Hare Hare. In the names of all other yugas you will find this vikrama and mukti, but here in the taraka-brahma-nama for the Kali-yuga you will only find prema, only prema. That is said: bhakti-pade-mukti-dasi -- mukti is the maidservant standing at the doorstep of prema-bhakti. Those who are really intelligent persons, those who only de sire to accept the essence, chant this mantra: Hare Krsna Hare Krsna Krsna Krsna Hare Hare, Hare Rama Hare Rama Rama Rama Hare Hare. One can chant in any place, at any time and there is no restriction at all.