Diksha-initiation:

The definition of diksha:

divyaṁ jñānaṁ hy atra mantre bhagavat-svarūpa-jñānam,

tena bhagavatā sambandha-viśeṣa-jñānañ ca

– Bhakti-sandarbha, Anuccheda 283

Divya-jñāna is transcendental knowledge contained within a mantra which reveals the form and identity of the Supreme Lord (bhagavat-svarūpa) as well as knowledge of the sādhaka-jīva’s particular relationship with the Lord.

In his Bhakti-Sandarbha (283) Srimat JivaGoswâmipad quotes the shâstra to describe the greatness of initiation

— “The âchâryas who know the truth define ‘dikshâ’ as that which bestows divine knowledge and destroys all sins.”

Sri Jivapad adds: “Here ‘divine knowledge’ means the knowledge about the Lord’s form which lies within the mantra, along with special knowledge about our relationship with the Lord.”

“The form of the living entity is that he is Krishna’s eternal servant. He is Krishna’s tatastha-shakti and so he is both different and non-different from Him.”– (C.C.)

Diksha-mantra:

Of all the different mantras that have been mentioned by the shastras in connection with diksh, the Sri Krishna-mantra is the most important, because Sri Krishna is Swayam Bhagavan and is the origin of all divine forms.

Sri Krishna performs divine pastimes in three Holy Abodes – Vrindavana, Mathura and Dwaraka. The greatest quality of Sri Bhagavan´s sweetness  is manifest in Sri Vrindavana,  alone where Sri Krishna plays like a cowherd boy.

Therefore the mantras in connection with this Vrindavana-lila are the greatest.

Then again,  the 10-syllable and the 18-syllable ‘Gopi-janavallabh’ mantra, that induce the topmost rasa (that of madhurya lila), are the greatest of all. Although these mantras are all present in sacred books, the chanting of those will yield no fruit without initiation. We must receive the mantra from the sadguru.

The mantra is non-different from Śrī Guru and from Śrī Krishna:

yo mantraḥ sa guruḥ sākṣāt yo guruḥ sa hariḥ svayam

gurur yasya bhavet tuṣṭas tasya tuṣṭo hariḥ svayam

– Hari Bhakti Vilasa 4.353

The mantra (received from Śrī Guru) is the Guru himself, and Śrī Guru is directly the Supreme Lord Krishna. There is no difference between Śrī Guru, the mantra given by him, and Śrī Hari. He with whom Śrī Guru is pleased, also obtains the pleasure of Śrī Krishna Himself.

Diksha initiation makes the devotee spiritual: 

prabhu kahe, vaiṣṇava-deha ‘prākṛta’ kabhu naya

‘aprākṛta’ deha bhaktera ‘cid-ānanda-maya’

dīkṣā-kāle bhakta kare ātma-samarpaṇa

sei-kāle kṛṣṇa tāre kare ātma-sama

sei deha kare tāra cid-ānanda maya

aprākṛta-dehe tāṅra caraṇa bhajaya

– CC Antya 4.192-3

Śrī Caitanya Mahāprabhu said, “The body of a devotee is never material. It is considered to be transcendental, full of spiritual bliss. At the time of initiation, when a sādhaka fully surrenders to Śrī Guru, Kṛṣṇa makes him like Himself. He transforms the devotee’s body into spiritual substance; the sādhaka then worships the Lord in that spiritualized body.”

Diksha is absolutely necessary:

guru-dīkṣā vihinasya na siddhim na sad-gatim

tasmat sarva-prayatnena guruṇā dīkṣitaṁ bhavet

– Purāṇa vakya

Without proper dīkṣā from Śrī Guru, no one can attain perfection or the supreme destination. Therefore, with utmost care and attention one should accept dīkṣā initiationfrom Śrī Guru.

Famous question:

When the Hare Krishna mantra is called the Mahamantra, then will we not attain perfection by taking this mantra alone? And why will we not achieve ‘diksha’ – which is our goal – by taking this mantra? The answer to this is that the Hare Krishna-mantra is called the Mahamantra because it is more powerful than any other mantra in bestowing prem. Still, the rule is that a diksha-mantra must have a dative case-ending and the six standard sequences that form a certain pattern of composition. Since the Mahamantra does not have this it is not a diksha-mantra. We should know that when we take Harinam-initiation before diksha, the Mahamantra blesses us by giving us a sadguru and he instructs us about bhajan; after taking diksha the result of chanting the Holy Name is prema.