According to Devi Bhagavatam Manasa is the mind born daughter of sage Kashyapa and Kadru(Mother of Manasa Devi) that is the reason behind her name Manasa Devi is also known as the snake Goddess who is worshipped mainly in Bengal and other North-Eastern states of India. It is believed that Goddess Manasa is the one who controls all the snakes on Earth and a snake bite can be cured by worshipping Her. People also worship Goddess Manasa for fertility and prosperity.
Here is the story of Goddess Manasa from Devibhagavatam
Manasâ is the mind-born daughter of Maharsi Kas’yapa; hence she is named Manasâ; or it may be She who plays with the mind is Manasâ. Or it may be She who meditates on God with her mind and gets rapture in Her meditation of God is named Manasâ. She finds pleasure in Her Own Self, the great devotee of Visnu, a Siddha Yoginî. For three Yugas She worshipped S’rî Krisna and then She became a Siddha Yoginî. S’rî Krisna, the Lord of the Gopîs, seeing the body of Manasâ lean and thin due to austerities, or seeing her worn out like the Muni Jarat Kâru called her by the name of Jarat Kâru. Hence Her name has come also to be Jarat Kâru. Krisna, the Ocean of Mercy, gave her out of kindness, Her desired boon; She worshipped Him and S’rî Krisna also worshipped Her. Devî Manasâ is known in the Heavens, in the abode of the Nâgas (serpents), in earth, in Brahmâloka, in all the worlds as of very fair colour, beautiful and charming. She is named Jagad Gaurî as she is of a very fair colour in the world. Her other name is S’aivî and she is the disciple of S’iva. She is named Vaisnavî as she is greatly devoted to Visnu. She saved the Nâgas in the Snake Sacrifice performed by Pariksit, she is named Nages’varî and Nâga Bhaginî and She is capable to destroy the effects of poison. She is called Visahari. She got the Siddha yoga from Mahâdeva; hence She is named Siddha Yoginî; She got from Him the great knowledge, so she is called Mahâ Jñanayutâ, and as she got Mritasamjîvanî (making alive the dead) she is known by the name of Mritasanjîvanî. As the great ascetic is the mother of the great Muni Âstîk, she is known in the world as Âstîka mâtâ. As She is the dear wife of the great high-souled Yogi Muni Jarat Kâru, worshipped by all, she is called as Jarat Kârupriya, Jaratkâru, Jagadgaurî, Manasâ, Siddha Yoginî, Vaisnavî,
âga Bhaginî, S'aivi, Nages’varî, Jaratkârupriyâ, Âstikamâtâ, Visahari, and Mahâ Jñanayutâ; these are the twelve names of Manasâ, worshipped everywhere in the Universe. He who recites these twelve names while worshipping Manasâ Devî, he or any of his family has no fear of snakes. If there be any fear of snakes in one’s bed, if the house be infested with snakes or if one goes to a place difficult for fear of snakes or if one’s body be encircled with snakes, all the fears are dispelled, if one reads this stotra of Manasâ. There is no doubt in this. The snakes run away out of fear from the sight of him who daily recites the Manasâ stotra. Ten lakhs of times repeating the Manasâ mantra give one man success in the stotra. He can easily drink poison who attains success in this stotra. The snakes become his ornaments; they carry him even on their backs. He who is a great Siddha can sit on a seat of snakes and can sleep on a bed of snakes. In the end he sports day and night with Visnu.
According to Hindu Mythology she is sister of Vasuki(King of snakes)
Manasā is the sister of Vasuki, king of the snakes; the wife of Jaratkāru, a sage; and being the queen of the snakes is regarded as the protectress of men from those reptiles.