Durga is an incarnation of the Mother goddess or Devi.

She is a superheroine depicted as having 10 arms, riding a lion or a tiger, carrying weapons (including a Lotus flower), maintaining a meditative smile, and practicing mudras, or symbolic hand gestures.

She manifested when evil forces threatened the very existence of the gods. To destroy the demons all the gods offered her a part of  their radiance.

She carries powerful weapons -the chakra of Vishnu and a trident from Shiva. Durga killed the powerful demon of anger called Mahisha and all his commanders.

Durga means invincible. The syllable 'du' is synonomous with the four demons of poverty, famine, sufffering and evil habits.the 'r' refers to diseases and the 'ga' is the destroyer of demons.

An embodiment of creative feminine force (Shakti), Durga exists in a state of svātantrya (dependence on the universe and nothing/nobody else, i.e., self-sufficiency) and fierce compassion. Durga is considered by Hindus to be an aspect of Kali, and the mother of Ganesha, and Kartikeya.She is thus considered the fiercer, demon-fighting form of Shiva's wife, goddess Parvati. Durga manifests fearlessness and patience, and never loses her sense of humor, even during spiritual battles of epic proportion.

The word Shakti, means divine feminine force, 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 god Shiva, on whose body she is often seen standing.

Durga's form is blindingly bright, as a radiant goddess (devi), with three lotus-like eyes, ten powerful hands, lush hair with beautiful curls, a red-golden glow from her skin and a quarter moon on her forehead. She wears a shiny attire emitting fierce rays. Her ornaments were carved beautifully of gold, with ocean pearls and precious stones embedded in it.
Durga painting Orissa, India

As a Goddess, Durga's feminine power contains the energies of the gods. Each of her weapons was gifted to her by various gods: Rudra's trident, Vishnu's discus, Indra's thunderbolt, Brahma's kamandalu, Kuber's Ratnahar, etc.

The Legend
According to the narrative from the Devi Mahatmya story of the Markandeya Purana text, Durga was created as a warrior goddess to fight an asura, (an inhumane force/demon) named Mahishasur. 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. Eventually, since only a woman could conquer him, the gods went down to the river Ganges and prayed the mantra, "Om Namo Devaye", imploring of the great mother goddess Devi to save their realm from ruin. They were blessed with her compassion when the goddess Durga was born out of the river to fight Mahishasur.

It is said that upon initially encountering Durga, Mahishasura tried to marry her, because of her strikingly beautiful radiance. However, Durga was not distracted or fooled - she graciously refused and proceeded towards battle.

And the terrible Mahishasur rampaged against her, changing forms many times. First he was a buffalo demon, and she slayed him with her sword. The he changed forms and became an elephant that tied up the goddesses' tiger and began to pull it towards him. The goddess cut off his trunk with her Khorgo. The demon Mahishasur continued his terrorizing, taking the form of a lion, and then the form of a man, but both of them were gracefully slain by the goddess Durga.

Then Mahishasur began attacking once more, starting to take the form of a buffalo again. The patient goddess became very angry, and as she sipped divine wine from a cup she smiled and proclaimed to Mahisasur in a colorful tone - "Roar with delight while you still can O illiterate demon, because when I will kill you after drinking this, the gods themselves will roar with delight". When Mahashaur had half emerged into his buffalo form, he got paralyzed by the extreme light emitting from the goddess's body. The goddess then resounded with laughter before cutting Mahisasur's head down with her Khorgo.

And thus Durga slayed Mahisasur... thus is the power of the fierce compassion of Durga.

From http://en.wikipedia.org/wiki/Durga Illustration detail from The Goddess Oracle Copyright Hrana Janto, used by permission of the artist. www.goddessoracle.com  www.hranajanto.com