Does Lord Ganesha really have an elephant head or is it simply part of the iconography? Usually any Hindu Devata iconography is based on philosophical understanding of the Devata. The elephant trunk is most probably part of the Sanskrit syllable AUM since AUM stands for both nirguna and saguna Brahman. The common people many centuries ago did not understand the philosophical import and wanted some simple explanation. The Puranic stories were written to give concrete explanation to those people.
Tales of Imagination
Brahma tells Narada "This brief account of the manifestation of the
Lord is what is called the Bhagavata. TheSupreme Being Himself gave
the knowledge of it to me. I have also given to you a brief account of
the Lord's glories and attributes. You elucidate it with the help of
your imaginative power in a way that will generate devotion in the
mind of men for Sri Hari who is the soul and support of all."
Bhagavata Purana II.8.51-52
Actually there are several Puranic stories about Lord Ganesha and his elephant head. These stories are:
- Once Parvati, just for fun, prepared an image of a child with an elephant's head, out of the unguents smeared over her body and threw
it into the river Ganga. It came to life. Both Ganga and Parvati
addressed the boy as their child. Hence Lord Ganesha is known as
Dvaimatura, 'one who has two mothers';
- Parvati prepared the image of a child out of the scurf from her body, endowed him with life and ordered him to stand guard before her
house. When Siva wanted to enter the house he was rudely prevented by
Ganesha. Siva became Rudra and got him beheaded. Seeing that Parvati
was inconsolable, Siva grafted an elephant's head on the body of the
boy and gave him life. Siva appointed this new-found son as the head
of all his retinues, who thus became 'Ganapati'.
- He sprang from Siva's countenance which represents akashtattva (principle of ether). His captivating splendour made Parvati react
angrily and curse him, resulting in the elephant head; and
- Ganesha was originally Krishna himself in the human form. When Sani, the malevolent planet spirit gazed at him, his head got
separated and flew to Goloka. The head of an elephant was subsequently
grafted on the body of the child.
[Hindu Gods and Goddesses by Swami Harshananda]
All these Puranic stories are taken from the book 'Hindu Gods and Goddesses' by Swami Harshananda. The learned Swami gives several views regarding the meaning of the elephant head. First he points out that Ganapati had gained de facto recognition in the hearts of millions of votaries over several centuries long before the Puranas were written. Several Puranic stories reflect the struggle by various Puranic authors to give de jure recognition to Ganapati! He gives the following possible meanings of the elephant head:
'Gana' means category. Everything that we perceive through our senses
or grasp through our mind can be expressed in terms of category. The
principle from which all such categories have manifested themselves is
Ganapati, the Lord of categories. In effect, it means the origin of
the whole creation, God Himself; A common Sanskrit word to denote
elephant is 'Gaja'. Hence the name Gajanana or Gajamukha
(elephant-faced) for Ganapati. But the word 'Gaja' has a deeper
connotation. 'Ga' indicates 'Gati', the final goal towards which the
entire creation is moving. 'Ja' stands for 'Janma' or birth or origin.
Hence 'Gaja' signifies God from whom the worlds have come out and
towards whom they are progressing, to be ultimately dissolved in Him.
The elephant head is thus purely symbolical and points to this truth;
A factor we observe in creation is its two-fold manifestation as the
microcosm (Suksmanda) and macrocosm (Brahmanda). Each is a replica of
the other. They are one in two and two in one. The elephant head
stands for the macrocosm and the human body for the microcosm. The two
form one unit. Since the macrocosm is the goal of microcosm, the
elephant part has been given greater prominence by making it the head.
The elephant-human form of Ganapati is the iconographical
representation of the great Vedantic dictum, 'tat-tvam-asi'(which
means You the apparently limited individual are in essence the Cosmic
Truth, the Absolute). The elephant stands for the cosmic whereas the
human stands for the individual.
REF: Hindu Gods and Goddesses by Swami Harshananda