Bhagavan is a fairly complex term used in Hinduism. 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.
"This Bhagavan, the worshipable Supreme Personality of Godhead is Vrajendra-nandana, the son of Nanda Maharaja. Vrindavana is His abode. The path conceived of by the gopis is the topmost method of worship. Shrimad Bhagavatam is the spotless Purana. Love of God (Krishna-prema) is the superlative human achievement. This is the view of Shri Chaitanya Mahaprabhu, for which we have the highest respect and love." (Chaitanya-mata-manjusha 1.1.1 by Vishvanatha Chakravarti Thakura).
