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