Bhagavān (Sanskrit: भगवान्, Bhagavān) is an epithet for deity, particularly for Krishna and other avatars of Vishnu in Vaishnavism, as well as for Shiva in the Shaivism tradition of Hinduism, and is used by Buddhists to refer to the Buddha. In north India, Bhagavān also represents the concept of abstract God to Hindus who are religious but do not worship a specific deity.
The term Bhagavān does not appear in Vedas, nor in early or middle Upanishads. The oldest Sanskrit texts use the term Brahman to represent an abstract Supreme Soul, Absolute Reality, while using names of deities like Krishna, Vishnu, Shiva to represent gods and goddesses. The term Ishvara appears in later Vedas and middle Upanishads where it is used to discuss spiritual concepts. The word Bhagavān is found in later era literature, such as the Bhagavad Gita and the Puranas.
In Bhakti school literature, the term is typically used for any deity to whom prayers are offered; for example, Rama, Ganesha, Kartikeya, Krishna, Shiva or Vishnu. Often the deity is the devotee's one and only Bhagavan. Bhagavan is male in Bhakti traditions, and the female equivalent of Bhagavān is Bhagavatī. To some Hindus the word Bhagavan is an abstract, genderless God concept.
In Buddhism's Pali scriptures, the term is used with Gautama Buddha, referring to him as Bhagavān Buddha (translated with the phrase 'Lord Buddha' or 'The Blessed One') and Bhagavān Shakyamuni. The term Bhagavān is also found in other Theravada, Mahayana and Tantra Buddhist texts.
Bhagavān is generally translated as idol or idol. In modern usage, Bhagavān is synonymous with Ishvara, Devatā, Hari or Prabhu, in some schools of Hinduism. Bhagavan is alternatively spelled as Bhagvān, Bhagwan or Bhagawan. The word is, in some sects, used as an honorific title for a spiritual leader considered fully enlightened by the sect. The word is also a proper noun and used as a first name for boys.
Bhagavān literally means "fortunate, blessed" (from the noun bhaga, meaning "fortune, wealth", cognate to Slavic bog "god", Polish bogaty Serbo-Croatian bogat, Russian богатый (bogatyj) "wealthy"), and hence "illustrious, divine, venerable, holy", etc.
The Vishnu Purana defines Bhagavān as follows,
उत्पत्तिं प्रलयं चैव भूतानामागतिं गतिम्
वेत्तिं विद्यामविद्यां च स वाच्यो भगवानिति
He who understands the creation and dissolution, the appearance and disappearance of beings, the wisdom and ignorance, should be called Bhagavān.— Vishnu Purana, VI.5.78 
Knowledge is of two kinds, that which is derived from scripture, and that which is derived from reflection. Brahma that is the word is composed of scripture; Brahma that is supreme is produced of reflection. Ignorance is utter darkness, in which knowledge, obtained through any sense (as that of hearing), shines like a lamp; but the knowledge that is derived from reflection breaks upon the obscurity like the sun. (...) That which is imperceptible, undecaying, inconceivable, unborn, inexhaustible, indescribable; which has neither form, nor hands, nor feet; which is almighty, omnipresent, eternal; the cause of all things, and without cause; permeating all, itself unpenetrated, and from which all things proceed; that is the object which the wise behold, that is Brahma, that is the supreme state, that is the subject of contemplation to those who desire liberation, that is the thing spoken of by the Vedas, the infinitely subtile, supreme condition of Vishnu.
That essence of the supreme is defined by the term Bhagavat. The word Bhagavat is the denomination of that primeval and eternal god: and he who fully understands the meaning of that expression, is possessed of holy wisdom, the sum and substance of the Vedas. The word Bhagavat is a convenient form to be used in the adoration of that supreme being, to whom no term is applicable; and therefore Bhagavat expresses that supreme spirit, which is individual, almighty, and the cause of causes of all things. The letter Bh implies the cherisher and supporter of the universe. By ga is understood the leader, impeller, or creator. The dissyllable Bhaga indicates the six properties, dominion, might, glory, splendour, wisdom, and dispassion. The purport of the letter va is that elemental spirit in which all beings exist, and which exists in all beings. And thus this great word Bhagavan is the name of Vásudeva, who is one with the supreme Brahma, and of no one else. This word therefore, which is the general denomination of an adorable object, is not used in reference to the supreme in a general, but a special signification. When applied to any other (thing or person) it is used in its customary or general import. In the latter case it may purport one who knows the origin and end and revolutions of beings, and what is wisdom, what ignorance. In the former it denotes wisdom, energy, power, dominion, might, glory, without end, and without defect.— Vishnu Purana, VI.5 
Bhagavan is related to the root Bhaj (भज्, "to revere, adore"), and implies someone "glorious, illustrious, revered, venerable, divine, holy (an epithet applied to gods, holy or respectable personages)". The root Bhaj also means "share with, partake of, aportion". Clooney and Stewart state that this root, in Vaishnava traditions, implies Bhagavan as one perfect creator that a devotee seeks to partake from, share his place with, by living in god, in the way of god, the loving participation between the two being its own reward.
The Vedic texts neither mention nor provide a basis to explain the origin of the Bhagavān concept.
The root of Bhagavan, Bhaga is mentioned in the Mundaka Upanishad, but it does not mean or imply Bhagavan:
The Mundaka Upanishad then answers this question in two parts over verses 1.1.4 through 3.2.11 - lower knowledge and higher knowledge. The lower knowledge includes Vedas, phonetics, grammar, etymology, meter, astronomy and ceremony rituals. The higher knowledge, the Upanishad asserts, is Self-knowledge and realizing its oneness with Brahman - the one which cannot be seen, nor seized, which has no origin, no qualities, no hips, nor ears, no hands, nor feet, one that is the eternal, all-pervading, infinitesimal, imperishable. The word Bhagavan does not appear in the Mundaka Upanishad and other early or middle Upanishads.
Later and medieval era Upanishads mention Bhagavān. For example, the very first verse of the Kali-Saṇṭāraṇa Upaniṣhad includes it, as follows,
द्वापरान्ते नारदो ब्रह्माणं जगाम कथं भगवन् गां पर्यटन् कलिं सन्तरेयमिति
At the start of the Dvapara [Yuga] Narada went to Brahma and asked, "O Lord, how shall I, roaming over the earth, be able to overcome the effects of Kali [Yuga]?"
Kali-Saṇṭāraṇa, a minor Upanishad, then proceeds to disclose, among other things, two Bhagavan names in the Hare Krishna mantra in verse 2, which is sung by International Society for Krishna Consciousness (ISKCON) devotees.
In Bhagavata Dharma it denotes Narayana Vasudeva's four vyuha formations. Ishvara or God is called Bhagavan and the person consecrated to Bhagavan is called a Bhagavata. The Bhagavata Purana (I.iii.28) identifies Krishna as Narayana, Vāsudeva, Vishnu and Hari – Bhagavan present in human form. Bhagavan is the complete revelation of the Divine; Brahman, the impersonal Absolute, is unqualified and therefore, never expressed; Paramatman is Bhagavan in relation to Prakṛti and the Jiva; And, the Yoga of Devotion implies that if a Bhagavata, the devotee of Bhagavan, seeks and longs for Bhagavan, then Bhagavan too seeks his devotee in equal measure, for there can be no Yoga of knowledge without a human seeker of the knowledge, the supreme subject of knowledge and the divine use by the individual of the universal faculties of knowledge.
श्रीभगवानुवाच । कुतस्त्वा कश्मलमिदं विषमे समुपस्थितम् । अनार्यजुष्टमस्वर्ग्यमकीर्तिकरमर्जुन ॥ २-२॥
Shri Bhagavan said, "from where had this weakness arisen, at this inconvenient time?
It is not noble, neither will it lead you to heaven, nor will it earn you valor, O Arjuna.
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The Bhāgavat traditions of Hinduism invoke Bhagavan in Narayan Upakheyam and in Bhagavad Gita of Bhishma Parva of the Mahabharata. The devotion to Lord Vishnu (identified as Vasudeva in Mahabharata) is described as ten incarnations of Vishnu. It introduced the Chatur – vyuha concept and laid emphasis on the worship of five Vrisini-warriors, reached the peak of its popularity during the Gupta Period.
In Hinduism, the word, Bhagavān, indicates the Supreme Being or Absolute Truth conceived as a Personal God. This personal feature indicated by the word Bhagavān differentiates its usage from other similar terms such as Brahman, the "Supreme Spirit" or "spirit", and thus, in this usage, Bhagavan is analogous to the Christian conception of God the Father. In Vaisnavism, a devotee of Bhagvān Krishna is called a Bhāgavata.
The Bhagavata Purana (1.2.11) states the definition of Bhagavān to mean the supreme most being:
Bhagavān used as a title of veneration is often directly used as "Lord", as in "Bhagavān Rama", "Bhagavān Krishna", "Bhagavān Shiva", etc. In Buddhism and Jainism, Gautama Buddha, Mahavira and other Tirthankaras, Buddhas and bodhisattvas are also venerated with this title. The feminine of Bhagavat is Bhagawatī and is an epithet of Durga and other goddesses. This title is also used by a number of contemporary spiritual teachers in India who claim to be Bhagavan or have realized impersonal Brahman.
Bhakti (devotion to God) consists in actions performed dedicated to the Paramatman, the individuated existence which has free-will and who is the final cause of the world; the Vedic Rishis describe the goals originated from God as Bhagavān, the Ananda aspect of God where God has manifested His personality is called Bhagavān when consciousness (pure self-awareness) aligns with those goals to cause the unified existence and commencement of works follow.
Some Buddhist texts, such as the Pali suttas, use the word "Bhagavā" for Buddha, meaning as 'the fortunate one'. The term "Bhagavā" has been used in Pali Anussati or recollections as one of the terms that describes the "Tathāgata" as one full of good qualities, as arahant, sammā-sambuddho and sugato (Dīgha Nikāya II.93).
In the Buddha Anussati, Bhagavan is defined the following way:
Several Tibetan Buddhist tantra texts use the word Bhagavān. For example, the Pradipoddyotana manuscript of Guhyasamāja tantra-Samdhivyakarana uses the word Bhagavān, which Alex Wayman translates as "Lord". The text, elsewhere refers to Bhagavan Sarvatathagatakayavakcittadipatih, which John Campbell translates as "Lord, Master of the Vajras of Body, Speech, and Mind of all Buddhas." Elsewhere, it states,
Thereupon, having made offerings and bowing down to the Bhagavan,
The Lord of Body Speech and Mind of all Tathagatas,
All the Bhagavan Tathagatas spoke thus:
Glorious One, pray explain the essence,
The unexcelled Bodhicitta,
The secret of all Tathagatas,
The supreme of Body Speech and Mind.— Pradipoddyotana, II. 1 
Laṅkāvatāra Sūtra, a sutra of Mahāyāna Buddhism, for example, uses the word Bhagavān over three hundred times, which is either left untranslated by scholars, or translated as "Lord or Blessed One". The devotional meditational text Sukhavati Vyuhopadesa by Vasubandhu uses the term Bhagavān in its invocations.
The term Bhagavān is found in liturgical practices of Theravada Buddhism, where it is used as an epithet that means the "Blessed One". Examples of such usage is found in Sri Lanka's Bodhi Puja (or Atavisi Buddha Puja, Worship of the Twenty Eight Buddhas).
A word derived from Bhagavan is documented epigraphically from around 100 BCE, such as in the inscriptions of the Heliodorus pillar; in which Heliodorus, an Indo-Greek ambassador from Taxila to the court of a Shunga king, addresses himself as a Bhagavata ("Heliodorena bhagavatena", Archaeological Survey of India, Annual Report (1908-1909)):
This Garuda-standard of Vasudeva (Vishnu), the God of Gods was erected here by the Bhagavatena (devotee) Heliodoros, the son of Dion, a man of Taxila, sent by the Great Greek (Yona) King Antialcidas, as ambassador to King Kasiputra Bhagabhadra, the Savior son of the princess from Benares, in the fourteenth year of his reign."[b]