Definition - What does Bhagavan mean?
Bhagavan is an epithet for "god," such as avatars of Vishnu in Vaishnavism and Shiva in the Shaivism tradition of Hinduism. The term denotes the Absolute Truth or the Supreme Being manifested as a personal god. It is this personal feature which differentiates the word from other similar terms, such as Brahman, which is Absolute Reality or the Supreme Spirit.
Neither the Vedic texts nor the early and middle Upanishads mention or explain the word, bhagavan. It is first found in later era literature, such as the Bhagavad Gita and the Puranas, where Ishvara (or God) is called Bhagavan, and the person consecrated to Bhagavan is called a bhagavata.
In some sects, the term is used as an honorific title for a spiritual leader considered fully enlightened by the sect. It is also used in yoga to refer to certain yogis.
Yogapedia explains Bhagavan
Bhagavan is generally translated to mean "lord" or "god," but it literally means "fortunate" or "blessed."
Some texts define bhagavan as the one who has the bhaga, or "majesty." Bhaga is described as having six qualities: dominion, might, glory, splendor, wisdom and dispassion. Some slight variations of the qualities listed can be found in different texts. Although everyone can claim to possess some degree of these qualities, only the Supreme personality of the Godhead can claim them all absolutely.
Bhagavan, Brahman and Paramatma (the Super Soul), are the three pillars of the Absolute Truth. It is stated that unless one understands all these features of the Absolute Truth, one's knowledge is imperfect. It is also said that the seekers of Brahman are called jnana yogis, while those whose goal is Paramatma are called yogis, and seeking/knowing the bhagavan is a privilege of Bhakti yogis or devotees.
Nowadays, it is customary to address yogis or spiritual gurus and masters as Bhagavan, as a sign of honor and profound respect. Sometimes it is claimed wrong to address someone as God, but others claim it as perfectly normal in Hindu traditions.