In Shakta tradition, the Ten Wisdom Goddesses (Maha means great; Vidya means knowledge) are important representations of the cosmic order revealed in the Todala Tantra. They each carry symbolic stories and reveal the various stages of spiritual evolution.
According to the Mahabhagvata Purana, the Mahavidyas manifested as a result of an argument between Shiva and Sati, the earlier incarnation of Devi Parvati.
Sati's father, King Daksha, disapproved of his daughter's love for Shiva. He was further incensed when Sati went on to marry Him. Daksha organized a great yagna (sacrificial ritual) to which he invited everyone except his daughter and son-in-law.
Furious, Sati insisted on attending the sacrifice, in spite of Shiva forbidding her from doing so. Her anger transformed Sati into a terrible presence, which multiplied into the ten Mahavidyas. These Goddesses jointly subdued Shiva's resistance and thereby, Sati proceeded ahead to attend the sacrificial ritual.
Each goddess represents an aspect of the divine mother.
Kali: Represents Saturn. Kali is the first of the Mahavidyas and the fiercest aspect of Goddess Durga. Kali is considered as the Goddess of time and change. She presides over the time before the creation of the universe. Kali is represented as the consort of Lord Shiva. Her abode is cremation grounds and her weapons are Kripana (Scimitar) and Trishul (Trident).
Tara: Represents Jupiter. Goddess Tara is the second Mahavidya. Tara, which means star, is seen as beautiful but perpetually self-combusting. Hence Goddess Tara is perceived as the personification of unquenchable hunger that propels life. Tara is the Goddess who offers ultimate knowledge and gives salvation and is also known as Neel Saraswati. Her weapons are Khadga, a sword and a pair of scissors.
Shodashi: Represents Mercury. Goddess Shodashi is also known as Tripura Sundari. As the name suggests Goddess Shodashi is the most beautiful in all three worlds. In Mahavidya, she represents the Goddess Parvati or is known as Tantric Parvati. Goddess Shodashi is also known as Lalita and Rajarajeshwari which means "the one who plays" and "queen of queens" respectively.
Bhuvaneshwari: Represents the Moon. Bhuvaneshvari is the fourth of the ten Mahavidya Goddesses. She is also known as the World Mother and personifies the whole universe. As the name suggests she is the queen of all the worlds and rules the whole universe.
Bhairavi: Represents Lagna. Bhairavi is the fifth of the ten Mahavidya Goddesses. Bhairavi is a fierce and terrifying aspect of the Goddess and is hardly indistinguishable from Kali. Goddess Bhairavi is the consort of the Bhairava which is the fierce manifestation of Lord Shiva associated with destruction.
Chinnamasta: Represents Rahu. Chinnamasta is the sixth of the ten Mahavidya Goddesses and is known as the self-decapitated Goddess. She is also known as Prachanda Chandika.
Dhumvati: Represents Ketu. Dhumavati is the seventh of the ten Mahavidya Goddesses. Devi Dhumavati is an old widow and is associated with things considered inauspicious and unattractive. She is always hungry and thirsty and initiates quarrels. In characteristics and nature she is compared with Goddess Alakshmi, Goddess Jyeshta and Goddess Nirriti. All these three Goddesses are the embodiment of negative qualities but at the same time worshipped at special timings of the year.
Bagalamukhi: Represents Mars. Bagalamukhi is the eighth of the ten Mahavidya Goddesses. Her name is the combination of Bagala and Mukhi. Bagala, which is a distortion of the original Sanskrit root Valga (वल्गा), means bridle. The headgear used to control a horse is known as a bridle. Hence Bagalamukhi means the Goddess who has the power to control and paralyze enemies. Due to her powers to capture and paralyze, she is also known as Devi of Stambhana.
Matangi: Represents the Sun. Matangi is the ninth of the ten Mahavidya Goddesses. Like Goddess Saraswati, she governs speech, music, knowledge and the arts. Hence Goddess Matangi is also known as Tantric Saraswati. Although Goddess Matangi is compared with Goddess Saraswati, She is often associated with pollution and impurity. She is considered an embodiment of Ucchishta (उच्छिष्ट) which means leftover food in hands and the mouth. Hence, she is also known as Ucchishta Chandalini and Ucchishta Matangini. She is described as an outcast and offered left-over and partially eaten food i.e. Ucchishta to seek her blessings.
Kamala: Represents Venus. Kamala is the tenth of the ten Mahavidya Goddesses. Goddess Kamala is considered the most supreme form of the goddess who is in the fullness of Her graceful aspect. She is compared to and considered to be Goddess Lakshmi. She is also known as Tantric Lakshmi. The goddess in the form of Kamala bestows prosperity and wealth, fertility, crops, and good luck. Hence she is Devi of both Dhan and Dhanya i.e. wealth and grains.
Source (Drik Panchang)