Vinayaka or Ganesh or Ganapathi or Vighneswara all indicate the Elephant-God, who is popular among young and old, and who is worshipped as the very first deity, before regularly beginning any ceremony or samskar, any yaga of yajna, any vow or fast or pilgrimage. He is the Lord of the ganas or divine forces, inside and outside the human body; He is the Lord, who masters and overwhelms vighna or obstacle, however imminent or eminent. This is the natural effect of the fact that Ganapathi is the God of Intelligence, vidya or buddhi.
Another name for Vinayaka is 'Vighneswara'. Easwara is one who is endowed with every conceivable form of wealth: riches, knowledge, health, bliss, beauty, etc. Vighneswara is the promoter of all these forms of wealth and removes all obstacles to their enjoyment. He confers all these forms of wealth on those who worship him. Vinayaka is described as "Prathama Vandana" (the first deity who should be worshiped). As everyone in the world desires wealth and prosperity, everyone offers the first place for worship to Vighneswara.
Ganapathi is a God revered in Tantric lore, and also, by various Vedic mantras. The elephant is proverbially the most intelligent among the mammals and it is vegetarian, indicating its sathwic nature. Ganapathi has the head of the elephant, for, it indicates the Intelligence through which obstacles in the path of achievement, secular as well as spiritual can be overcome. There is a popular verse, used on most occasions when Ganapathi is invoked. It mentions various attributes of this God: Suklambaradharam (wearing white vesture) is the first. This is the symbol of purity, for, ambara means also the sky (space, ether), the akasa of the heart. Ganapathi is pure, having universal love and compassion. Vishnu is the second attribute, ascribed to Him.
Vishnu means that He is present everywhere, at all times. Sasivarnam is the third adjective used. Of the complexion of ash, or Vibhuti, that is to say, glowing with spiritual splendor, with the majesty of spiritual attainments, achievements and potentialities. These are also called Vibhutis, for, in the Gîtâ, we find Krishna saying, 'wherever you see Power, Glory, Majesty (Vibhuti), know that it is Mine'! [see: BG : 10-41] Ganesha is bathed in His Divine Glory; that is the significance of the attribute Sasivarnam.
Chathurbhuja (four-handed) is the next fourth denotation. This means that apart from the two visible hands, He has two invisible hands, that are available for the two divine uses of: 1. Blessing the devotee and 2. Guarding him from danger.
The last fifth of the descriptive word is Prasannavadanam (of bright countenance). The countenance depicts the inner calm, happiness and balance, inner grace and mercy, the consciousness of strength and sovereignty.
What is the esoteric meaning of Ganesha's elephant head? The elephant is noted for its acute intelligence. Ganesha's elephant head symbolizes sharpness of intellect and the highest power of discrimination. Because of the purity of his intellect, Vinayaka is also called the giver of buddhi (intellect). He responds to the prayers of devotees and hence is known as Siddhi Vinayaka (the Vinayaka who grants what is sought).
In a forest, when an elephant moves through the jungle, it clears the way for others to follow. Likewise, by invoking Ganesha, the path is cleared for our undertakings. The elephant's foot is so large that when it moves it can stamp out the footprints of any other animal. Here, again, the symbolic meaning is that all obstacles in the way will be removed when Ganesha is accorded the place of honor. The journey of life is made smoother and happier by the grace of Ganesha.
Vighneswara is also regarded as one endowed with the wisdom of the elephant. The elephant is noted for its supreme intelligence. it is also known for its absolute loyalty to its master. The direct proof of this is Sai Githa (Bhagavan's elephant). Ordinarily hundreds of cars will be passing on the road. Sai Githa will take no notice of them. But when Swami's car happens to pass that way, she will instinctively notice it, She will rush to the road raising her familiar cry. What love for Swami! It will be no exaggeration if faith is equated with the elephant.