Okay!! Now this is going to be a very big reply. And you need to be patient enough to read this. First things first. This cult what you call " Hare Krishnas" are acually a sect called as the International Society for Krishna Consciousness or (ISCON). They plan to propagate the idea of unification with the God of True Love. Bhagwan Sri Krishna. Now yes I know that you have a question about the origins of this sect and the story that surrounding it. Bhagwan Sri Krishna is a God followed by the Hindus, who are present and find their origins in India. We have religious and spiritual books like any other religion. The Bhagavadgita is a book which is revered as equivalently as Christians treat bible or Muslims treat Quran. Now the Indian mythology ( Purans) say that the world is divided into timelines (Yugas) There are different Yugas. Namely Sathya Yuga, Treta yuga, dwapar yuga and Kaliyuga. Now according to that we are now living in the Kaliyuga. The yugas before have had their own Incarnations of the divine power or the GOD. We in Hinduism belive that live is governed by three powers or in a more crude form by three Gods. The three powers that govern the life are called (Sristi- Sthithi-Laya , or Birth- life - Death) We designate three God's for this. This is similar to the ones you see in Greek Mythology. The Brahma is the creator, or the God who Governs birth.. Lord Vishnu is the one who governs and controls life and ways of life. Lord Shiva (Parameshwara or Rudra) Controls death. We believe in an after life and re birth cycle. The most commonly used word "KARMA" finds its origins from Indian puranas aswell. Now coming to the question of Lord Sri Krishna, the mythology goes on to define how life form came into existance on earth.
This is a quora post which tries to explain it
Matasya Avatar - > Life originated in sea , fish is the first Vertebrates
Kurma - > This represents Amphibians , could survive on both and and water
Varaha -> Wild land animal - complete transition from water to Land , next milestone in evolution
Narasimha -> conceptualisation of Homo Sapiens , the next big thing on the part of evolution
Vaman -> Short human being , Still not complete evolved
Parsuram -> Living in Jungles , Started Using weapons
Ram -> Moving to civil societies , learning to living as community , Various Skills developed , still not corrupt
Krishna -> Society advancement in Political field , more complexity added , manipulation , greed .
Budha \ Mahavir \ Balram\ Jagannath \ Mohini > On the path of enlightenment , more evolved human being , trying to find answers within (many people blasting me for incorrect representation of this avatar. Avatar is not important, the message is.)
Kalki ->Human advanced to the level of self - destruction . Check this link https://www.quora.com/How-real-are-the-10-avatars-of-Vishnu-dasavathara
Now Bhagawan Sri Krishna finds unique place in the mythology because his incarnation occured in the Dwapara yuga, the Yuga just before the one which we live in, and it is believed that the God's walked and talked like Humans in this Yuga and the Yuga before it. Lord Krishna in many ways represents the normal human behavior, we again have characterized the human behavior and his acts based on his indulgence to 'arishadvargas' According to Hindu theology Arishadvarga are the six passions of mind or desire that stop you from attaining moksha or salvation. They are: kama (lust), krodha (anger), lobh (greed), moha (attachment), mada(pride), and matsarya (jealousy).
So Lord Krishna indulges in these behaviors and carefully explains on how it affects life. The Hindu Theology finds its best places when the two great works The Ramayana and Mahabharatha are read. These two works( Said to be real and historic depictions of what has happened) when understood properly define life and answer all questions about the reasons of why we exist, why we are born to our parents, and why not in some other home. And in Mahabharatha you will find vivid portrayal of Bhagwan Sri Krishna. He is the reason behind everything. In what is called as the Yudda khaanda , a section in Mahabharatha ( This section is the depiction of the war Between the Pandavas and Kauravas) Here the Lord takes the side of the Pandavas. He becomes the Charioter for Arjuna. ( This war also is a depiction of the fight between the Good and the Bad/ or the fight between the right and the wrong and how truth prevails in the end). At the beginning of the war Arjuna sees his own relatives on the other side of the war front! The cousins he played with were the ones he had to kill now to attain victory. Arjuna feels devastated and drops his Weapons. This is when Lord Krishna tells him the Bhagawadgeetha). He explains about how our lives are destined to things which are way beyond our material lives and the deeds which we do as a routine. He explains about various forms of life, about how he is the controller of everything that happens and everything that is destined to happen)
The people who have studied Bhagavageetha say that it answers every question that you ever have In life and there isn’t anything that you don’t find answers for, in the Bhagawadgeetha. But it is for you to seek the answers.
However the Hare Krishna cult alone doesn’t represent the ideas of God and there have been instances where something materialistic has tarnished the actual messages of the God! The Learned men need to pick the real Gold from the dirt and the sand it lies in.
This was my sincere try to answer a few of the questions you may have had. We can discuss more
RE: Ever Met a Hare Krishna?