In Vedic philosophy, God is the Supreme Energy and the Supreme Energetic combined. In Sanskrit, Shakti or energy is feminine and Shaktiman or energetic is masculine. The feminine aspect of God is called Hara or Radha and the Masculine aspect of God is called Hari or Krishna.
The noun Hara in vocative becomes Hare, which means “O Supreme Divine Energy” or “Hey Radharani” and the noun Krishna remains the same in the vocative case, meaning “O Supreme Divine Energetic” or “Hey Krishna.”
Together, “Hare Krishna” is used for praying to God while we offer food and when we honor Prasad. The concept is that all the facility in the world that we are having, from water to sunlight to oxygen to foodgrains, are due to the mercy of God and so we acknowledge and thank God in our prayers. This mood purifies our body and mind and nourishes our intelligence.
Many people have the misconception that Vedic philosophy is polytheistic. Actually, if one deeply studies Vedic literature, without any doubt one can conclude that Vedic philosophy is monotheistic. Radha and Krishna are considered as the Supreme Divine Couple. All incarnations of God emanate from them. All other iswars or demigods work under the Supreme Divine Couple, and work as controller of different material energies. The concept is similar to different ministers taking charge of different departments under the Supreme President.
In Bhagavad Gita, Chapter 7 (Jnana-Vignana Yoga), Verse 23, Krishna says:
antavat tu phalam tesam
tad bhavaty alpa-medhasam
devan deva-yajo yanti
mad-bhakta yanti mam api
The translation is: “Men of small intelligence worship the demigods, and their fruits are limited and temporary. Those who worship the demigods go to the planets of the demigods, but My devotees ultimately reach My supreme planet.“
In Srimad Bhagavata Purana Canto 1, Chapter 3, Verse 28, after describing all incarnations of God, sage Vyasdev, who is the compiler of the all four Vedas and Upanishads, clearly states:
ete cāṁśa-kalāḥ puṁsaḥ
kṛṣṇas tu bhagavān svayam
It means, “All of the above-mentioned incarnations are either plenary portions or portions of the plenary portions of the Lord, but Krishna is the original Personality of Godhead.”
In RIG-VEDA Parishishta, it is mentioned:
Ekam Jyothi Rabhoo Dvidha
Radha Madhava Roopakam Parabrahma
The meaning is: “The one single effulgence Parabrahma is manifested in two ways as Radha and Madhava.”
Even in the puja of any demigod, it is customary to purify all the paraphernalia in the name of Vishnu (a form of Krishna). It is also customary to first offer food to Vishnu and then offer the remnants as Prasada to the demigod.