Hinduism as a religion involves the worship of not just one, but many deities. Each of these deities does not exist only as male or female Gods. In fact, every divine being has a male and a female form.
Their existence establishes essence only when they exist in their male and female avatars, signifying the complete circle of life. While the male avatar stands for mental power, the female avatar of a divine being represents the physical state of power or the ‘Shakti’. Lord Vishnu’s female avatar is known as Vaishnavi, Lord Indra’s female avatar is called Indrani, and Lord Brahma’s female avatar is called Brahmini. Similarly, Lord Ganesha too is complimented by his female avatar, Vinayaki, who is also called Ganeshvari.
The story about the female avatar of Lord Ganesha involves different interpretations. According to one interpretation, the demon Asura wanted Goddess Parvati to be his wife, and tried to obtain her by force. She appealed to her husband, Lord Shiva, who immediately raised His trident and impaled the demon. However, this demon possessed a certain magic power which turned every drop of his blood into another demon. The only way left to kill him was to ensure that not even a single drop of the demon’s blood would fall to the ground. Parvati was aware that every God is a combination of the male and female avatar, implying a combination of mental and physical state of power. Therefore, She called out to all the Shaktis who, on Her request, released. Their female energies to drink the blood of the demon so as to ensure his death. Among all these Shaktis, there was also present the female form of Lord Ganesha- Vinayaki or Ganeshvari.
This idea of a female elephant-headed deity is very important in the Tantric rituals, as these rituals prefer the worship of the divine female rather than the male dominant form. It was only with these tantric practices that the popularity of the female goddesses grew, as these practitioners believed in the generative powers of the female. The female is considered the source of all material resources that are responsible for the continuity of life. As a result, there now exists a divide between sages- one group that gives more importance to the mental strength, hence focusing worship on the male deities, and the other group veered towards material resources, hence focussing worship on the female deities.
Moreover, there are also a group of scholars who have yet another interpretation of the female Ganesha. The Puranic texts mention an elephant-headed companion of Lord Ganesha, called Malini, who was also the nursemaid of the Lord. This has made some scholars think that the female Ganesha was not a Goddess or a female avatar, but an exaggerated form of Malini, the nursemaid.
Despite all of these variances in the approach and debates among sages, it is important to note that this female Ganesha is acknowledged on the occasion of Vinayaki Chaturthi which falls on the fourth day after the new moon appears.