Bhagavan is a term which is commonly used,by several traditions. What is the definition of Bhagavan as per Vishnu Purana?
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
The same text defines Bhaga and provides the etymological roots as follows
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 subtle, 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 
The word Bhagavan is explained thus by Parasara Muni:
One who is full in six opulences, who has full strength, full fame, wealth, knowledge, beauty and renunciation, is Bhagavan, or the Supreme Personality of Godhead
The details of Kalyana Gunas of Bhagavan, are given in the answer