Durga is an incarnation of Devi or the Mother Goddess, a unified symbol of all divine forces. For Shaivas Durga is the wife of Shiva. For Vaishnavas and Shaktas Durga is another form of Uma or Parvati.
The Hindu Goddess Durga manifested when evil forces threathened the very existance of the Gods. To destroy these demons, all gods offered their radiance to her creation and each formed part of Durga's body. Durga also obtained very powerful weapons, such as the chakra from Vishnu and a trident from Shiva.
The name "Durga" in Sanskrit means "invincible". The syllable "du" is synonymous with the 4 devils of poverty, sufferings, famine and evil habits. The "r" refers to diseases and the "ga" is the destroyer of sins, injustice, irreligion, cruelty and laziness.
The word Shakti means divine feminine energy/force/power, and Durga is the warrior aspect of the Divine Mother. Other incarnations include Annapurna and Karunamayi (karuna = kindness). Durga's darker aspect Kali is represented as the consort of the god Shiva, on whose body she is often seen standing.
Durga Slays Mahishasura, Mahabalipuram sculpture.
As a goddess, Durga's feminine power contains the energies of the gods. Each of her weapons was given to her by various gods: Rudra's trident, Vishnu's discus, Indra's thunderbolt, Brahma's kamandalu, Kuber's Ratnahar, etc.
According to a narrative in the Devi Mahatmya story of the Markandeya Purana text, Durga was created as a warrior goddess to fight an asura (an inhuman force/demon) named Mahishasura. He had unleashed a reign of terror on earth, heaven and the nether worlds, and he could not be defeated by any man or god, anywhere. The gods went to Brahma, who had given Mahishasura the power not to be defeated by a man. Brahma could do nothing. They made Brahma their leader and went to Vaikuntha-the place where Vishnu lay on Ananta Naag. They found both Vishnu and Shiva, and Brahma eloquently related the reign of terror Mahishasur had unleashed on the three worlds. Hearing this Vishnu, Shiva and all of the gods became very angry and beams of fierce light emerged from their bodies. The blinding sea of light met at the Ashram of a priest named Katyan. The goddess Durga took the name Katyaayani from the priest and emerged from the sea of light. She introduced herself in the language of the Rig-Veda, saying she was the form of the supreme Brahman who had created all the gods. Now she had come to fight the demon to save the gods. They did not create her; it was her lila that she emerged from their combined energy. The gods were blessed with her compassion.
The four day long (Saptami to Dashami) Durga Puja is the biggest annual festival in Bengal, Orissa, Bihar, Assam and Nepal, where it is known as Dashain. It is celebrated likewise with much fervour in various parts of India, especially the Himalayan region, but is celebrated in various forms throughout the Hindu universe.
The day of Durga's victory is celebrated as Vijayadashami (Bengali), Dashain (Nepali) or Dussehra (Hindi) - these words literally mean "the Victory Tenth" (day).
In Kashmir she is worshipped as shaarika (the main temple is in Hari Parbat in Srinagar).
The actual period of the worship however may be on the preceding nine days (Navaratri) followed by the last day called Vijayadashami in North India or five days in Bengal (from the sixth to tenth day of the waxing-moon fortnight). Nine aspects of Durga known as Navadurga are meditated upon, one by one during the nine-day festival by devout Shakti worshippers.
In North India, the tenth day, signifying Rama's victory in his battle against the demon Ravana, is celebrated as Dussehra - gigantic straw effigies of Ravana are burnt in designated open spaces (e.g. Delhi's Ram Lila grounds), watched by thousands of families and little children.
In Mysore Karnataka, she is worshipped as Chamundeshwari, the patron goddess of the city during Dussehra
In Gujarat it is celebrated as the last day of Navaratri, during which the Garba dance is performed to celebrate the vigorous victory of Mahishasura-mardini Durga.
The Goddess Durga is worshiped in her peaceful form as Maha Gauri, The Fair Lady, Shree Shantadurga also known as santeri, is the patron Goddess of Goa. She is worshiped by all Goan Hindus.
In Maharashtra, Tulja Bhavani and Ambabai is worshiped as Mahishasur Mardini and is patron goddess of land. Bhavani is known as Tulaja, Amba, Renuka, Yamai, Saptshrungi, Jogai in different places of Maharashtra. She is inspirational goddess of Raja shivaji. As per legends, Bhavani revealed to Shivaji and blessed him to form a kingdom.