Bhagavan is a fairly complex term used in Hinduism, and by extension used in both Buddhism and Jainism as well. At its most basic, Bhagavan can be understood to represent a personal Supreme Being. Bhagavan is perhaps the manifestation of the divine in Hinduism that is closest to the Judeo-Christian understanding of a God.
While Brahman can also be thought of as representing a Supreme Being, it is generally used as a term to denote a more spiritual and abstract understanding of that being. Bhagavan, in contrast, is given a personality, with desires and defining characteristics. One way to think about the distinction between Brahman and Bhagavan would be to compare it to certain Christian views of God the Holy Ghost and God the Father, with the former being associated more with a general lifeforce, and the latter having a personality as Creator.
Bhagavan is also used as a title for many figures in Hinduism, Jainism, and Buddhism. In this context it can be understood simply as Lord, comparing the figure so named to the God-head of Bhagavan Himself. Female figures or goddesses may bear the same title in the feminine form, Bhagawati.
The title appears in Buddhism as a descriptor for the Buddha back to the early Pali Buddhist documents. This is most often translated simply as Lord Buddha or Lord Shakyamuni, where the original would be something like sakamunisa bhagavato. In Hinduism a number of the major gods are given the title Bhagavan, such as Bhagavan Shiva, Bhagavan Swaminarayan, Bhagavan Krishna, and Bhagawati Durga. In many English texts these would simply appear as Lord Krishna or the like.
In Hinduism the term Svayam Bhagavan may be used to differentiate the God-head from other gods who might bear the title of Lord. This can be translated roughly as meaning The Lord Himself, and may refer to Krishna in sects of Hinduism in which Krishna is viewed as the source of all divinity, or to Vishnu or Narayana in sects in which one of these figures is viewed as the ultimate source of the gods. In some sects, Svayam Bhagavan may even refer to a certain manifestation of Krishna, which can be understood as the god from which all the gods of our world spring, but who is subordinate to the triumvirate power of Vishnu, Brahma, and Shiva, who in turn are subordinate to Krishna’s form as ultimate God-head, or Svayam Rupa.
In the modern world, it is not uncommon to hear Bhagavan applied as a title to gurus and babas, as well as to the deities. This stems from the idea that God permeates all things of this world, and serves as a mark of respect for the ultimate teachers, acknowledging how visible the God-head has become in them. There are two recent and famous gurus who have borne this title. One is Bhagwan Shree Rajneesh, also known as Osho, a religious leader who died in 1990, and practiced an openly sexual form of Hinduism, propagating a movement known as neo-sannyas. The other is Bhagavan Das, a Yogi from California best known for helping to guide Ram Dass to a guru in his early spiritual awakening.