Meaning of the Mahamantra by Jiva Gosvami

Srila Jiva Gosvami reveals the meaning of each of the sixteen Names in the Maha-Mantra in consecutive order as follows:

Hare

sarva-ceta-harah krsnas tasya cittam haratyasau

vaidagdhi-sara-vistarair ato radha hara mata

Krsna steals the minds of everyone, yet Radha steals even His mind by Her divine expertise. Thus She is known as Hara.

Krsna

karsati sviyalavanya-murali-kala-nihsvanaih

sri radham mohana-gunalankrtah krsna iryate

He forcibly attracts Sri Radha with the sweet sound of His flute, therefore that Lord of all enchanting qualities is known as Krsna.

Hare

sruyate niyate rase harina harineksana

ekakini rahah-kunje hareyam tena kathyate

It has been heard that during the rasa-lila, doe-eyed Radha was stolen away by Krsna to be alone with Him in a secret forest bower. She is therefore known as Hara.

Krsna

anga-syamalima-stomaih syamalikrta-kancanah

ramate radhaya sardham krsno nigadyate

When Krsna sports with Radha, Her golden hue takes on the dark complexion of Krsna's skin. He is thus known as Krsna.

Krsna

krtvaranye sarah-srestham kantayanumatas-taya

akrsya sarva-tirthani taj-jnanat krsna iryate

In order to please Sri Radha, Krsna manifested the most wonderful lake (Syama-kunda) in Vrndavana. He then called all the holy rivers to fill it. He is thus known as Krsna.

Krsna

krsyate radhaya premna yamuna-tata-kananam

lilaya lalitas-capi dhiraih krsna udahrtah

By Her unsurpassed love, Radha charms He who performs wonderful lilas on the banks of the Yamuna. Therefore, those who are sober know Him as Krsna.

Hare

hrtavan gokule tisthann-aristam pusta-pungavam

sri haris tam rasad uccai rayatiti hara mata

While in Gokula, Sri Hari (Krsna) killed the demon known as Aristasura. During that time, Radha cried out to Him with great feeling and by doing so, She stole His mind. She is thus known as Hara.

Hare

hyasphutam rayati priti-bharena hari-cestam

gayatiti mata dhirair hara rasa-vicaksanaih

Filled with ecstatic love, Radha sometimes sings the glories of Hari's exploits quietly, and sometimes She sings them aloud. Those who are expert in the secrets of divine sentiments call Her Hara.

Hare

rasavesa-parisrastam jahara muralim hareh

hareti kirtita devi vipine keli-lampata

Due to the intense love of Sri Radha, Sri Hari becomes so captivated that His flute falls from His hand. With the desire to enjoy in the forest bowers with Krsna, Radha steals His flute. That goddess is thus famous as Hara.

Rama

govardhana-dari-kunje parirambha-vicaksanah

sri radham ramayamasa ramastena mato harih

Krsna, who is expert at embracing, sports with Radha in the forest groves or in the caves of Govardhana. Thus He is known as Rama.

Hare

hanti duhkhani bhaktanam rati saukhyani canvaham

hara devi nigadita maha-karunya-salini

That most merciful Radha destroys the miseries of Her devotees and gives them great happiness every day. Therefore that goddess is known as Hara.

Rama

ramate bhajato cetah paramananda-varidhau

atreti kathito ramah syamasundara-vigrahah

The minds of the devotees are continuously drowned in an ocean of supreme joy by seeing the beautiful dark form of Krsna. Therefore He is known by

the Name Rama.

Rama

ramayaty-acyutam premna nikunja-vana-mandire

rama nigadita radha ramo yutas taya punah

Radharani is known as Rama because She enjoys loving pastimes with Acyuta (Krsna) in a secret forest pavilion. Since He is always by Her side, He is known as Rama.

Rama

rodanair gokule davanalam asayati hyasau

visosayati tenokto ramo bhakta-sukhavahah

When the residents of Gokula were crying due to fear of the forest fire, Krsna immediately swallowed it and gave His devotees great joy. In this way, He is known as Rama.

Hare

nihantum asuran yato mathura-puram ity-asau

tadagamad-rahah-kamo yasyah sa'sau hareti ca

Sri Krsna went to Mathurapuri in order to destroy the demons. However, due to being captivated by the love of Radha, He later returned. Therefore She is known as Hara.

Hare

agatya duhkha-harta yo sarvesam vraja-vasinam

sri radha-hari-carito harih sri nandanandanah

When the son of Maharaja Nanda returned to Vraja, He took away the suffering of all the Vrajavasis. By His wonderful exploits, He steals the heart of Sri Radha. Thus He is known as Hari.

Also
http://radhanathswamiweekly.com/radhanath-swami-glorifies-jiva-goswami/