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 (karua = kindness). Durga’s darker aspect Kali is represented as the consort of the god Shiva, on whose body she is often seen standing.
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 Katyayan and Durga emerged from this pool of light. 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.
It is said that upon initially encountering Durga, Mahishasura underestimated her, thinking: “How can a woman kill me, Mahishasur—the one who has defeated the trinity of gods?”. However, Durga roared with laughter, which caused an earthquake which made Mahishasur aware of her powers.
And the terrible Mahishasura rampaged against her, changing forms many times. First he was a buffalo demon, and she defeated him with her sword. Then he changed forms and became an elephant that tied up the goddess’s lion and began to pull it towards him. The goddess cut off his trunk with her sword. 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 Durga.
Then Mahishasur began attacking once more, starting to take the form of a buffalo again. The patient goddess became very angry, and proclaimed to Mahishasur in a colorful tone—”Roar with delight while you still can, O illiterate demon, because when I will kill you, the gods themselves will roar with delight”. When Mahishasur had half emerged into his buffalo form, he was paralyzed by the extreme light emitting from the goddess’s body. The goddess then resounded with laughter before cutting Mahishasur’s head down with her sword.
Thus Durga slew Mahishasur, thus is the power of the fierce compassion of Durga. Hence, Mata Durga is also known as Mahishasurmardhini—the slayer of Mahishasur. According to one legend, the goddess Durga created an army to fight against the forces of the demon-king Mahishasur, who was terrorizing Heaven and Earth. After ten days of fighting, Durga and her army defeated Mahishasur and killed him. As a reward for their service, Durga bestowed upon her army the knowledge of jewelry-making. Ever since, the Sonara community has been involved in the jewelry profession.
Brahma, Vishnu and Shiva described the attainment of Shakti in the following manner
Meaning :- like a potter can not make pitcher without mud, a goldsmith can not make earrings without gold, similarly, universe can not be created without Shakti.
Meaning :- Like an intelligent person can not save the world without power, similarly, I (God) can not save the universe without Shakti.
This Shakti is Durga, Shiva, Paramba which is situated in Brahma, Shiva, Vishnu. It makes them capable for the duty and work. The nine incarnation of goddess are described as below
The 9 Durga are the symbol of the 9 power. She 9 incarnation are worshipped during the Navratri. These goddesses are the symbol of Brahmacharya, awareness, sacrifice, simplicity, knowledge, fearlessness, patience and sense of service.
Shailaputri
Shail Putri was the name of Parvati, the daughter of Himalaya. Vrishabsitha Mata has Trishul in her right hand and lotus in the left hand. She includes all substances, power and creature. Devi Uma is the power of lightness. She is the goddess of nature.
Brahmacharini
Brahma means universe and meditation. Here, Brahma stands for tenacity. Brahmacharini is the other form of Brahmashakti Dhatri Devi. She is Jyotirmayi and very magnificent. She has a rosary in right hand and stoup in the left hand. She performed meditation to have lord Shiva and got the name of Tapasyacharini. First of all she used to eat Bel leaves and then she left eating them and got the name Aparna.
Maa Chandraghanta
There are two phase of power, mentioned in scriptures. First is Unmani and the second one is Samni. Samni includes 16 arts. It has relation with Brahma Shakti. There is a half moon in shape of bell on the head of Devi Chandraghanta, hence, she got this name. She is a Lavanyamayi Divine Devi. She has a body of gold. She has 10 arms which have different scripture. She rides lion. And, she is always ready for any war. By the terrifying sound of her bell, everyone starts shaking. She is said to be goddess of best disciplines.
Kushmanda Devi
Kushmanda Devi is Adhishtatri goddess of wellness. She is the Aaddh Shakti and Brahma Shakti of universe. She is described as the one who created the universe through her smile. Hence, she is called the Kushmanda.
She has 8 arms. In 7 of her arms she holds stoup, bow, arrow, lotus, flower, urn having Amrit, Chakra and Gada. And, the eighth arm has a rosary. Goddess Kushmanda rides a lion. Seasonal change is because of her. She stays in the center of nature. Her treasure are medicines, herbs etc.
Skanda Mata
Goddess Skanda is the mother of Karthikeyen, son of Shiva. She has 4 arms. The 2 right arms have Uffar Skand and lotus flower. Left arm contains Vardmudra and lotus flower. She is Kamlasana, Shubvarna and rides on lion.
Katyayani
Maha Rishi Katyayan was born in the Gotra of Rishi Kavya, son of Maharishi Kat. Rishi Katyayan worshipped Paramba and received Devi Katyayni is form of daughter. This is the 6th incarnation of goddess. From Chaturthi of Ashwin Krishna Paksha to Navami, goddess received respect and worship from Rishi Katyayan. She is the power of mind. She has a divine form as of gold. goddess Katyayani has 3 eyes and 8 arms, and she rides lion.
Kalratri
Kalratri is the 7th form of Durga. her hairs are all open and scattered. She wears a necklace which is as bright as light. Her 3 eyes are circular like universe which emit bright light. Terrifying flame of fires are emitted from nose. She rides Gardha. The right arm is in blessing position.
The lower hand is in Abhey Mudra. Left arms have Kota and Khadag. She looks terrifying but gives auspicious fruits. She is also called Shubankari. She is the winner of Kal and known as Kali. She is Maha Shakti of Rudra Shiva. She wears 51 heads of dead demons on her neck.
Mahagauri
Mahagauri is the 8th Shakti. Compared with shell, moon and Kund flower. She has 4 arms. She wears white clothes. Right arms have Damru, Varmundra. She has a position for 8 years. Maha Gauri remains in a peaceful manner. She is called as Shakumbari Devi, Shatakshi, Trinetri, Durga, Chandi, Raktbeej Sangharini. She is Trishakti. At times she has Gaur Van(fair color) or at times Krishna Van(black color). She has different forms. She killed many demons so she is called Durga.
Siddhidatri
The giver of 18 Siddhi, 4 arms, rider of lion, having lotus flower is called Shakti. She holds lotus, Gada, Chakra, shell. She is dear to Vishnu and called Vaisnav Shakti. She is said to be Kamla Shakti, and is a symbol of wealth. She is beautiful and has 10 arms. Sidhidatri has many forms and has many weapons.
Sources : wikipedia & different online websites.