Shailputri goddess is the first among the nine incarnations of adishakti or durga who are worshipped in the days of navaratri. The first day of navaratri is dedicated to the goddess. Shailputri is the other name of Devi parvati, the wife of lord Shiva and mother of lord ganesh and lord kartikeya.
This name Shailputri is given to the goddess as she was born to the king of the mountains Himalaya, so sometimes she is also addressed as hemwati. The goddess actually is the rebirth of Devi sati, according to legends Devi sati was the wife of lord shiva and daughter daksha prajapati.
The father daksha loved his daughter but despised his son in law shiva as daksha was the king of kings and shiva used to live as an aghori among everyone be it the dev, danav, daitya, asura, Chandal, gandarva and yaksh, Mahadev did not see any arrogance of being noble than the other but daksha did.
Once, he arranged a great yagna and called all the gods in it but did not invited his own son in law lord shiva this angered Devi sati and she came to make realize her father to repent form his sin and invite Mahadev in the yagna but he refused and instead of inviting shiva he insulted him to a great extent which angered devi sati to great extent and to make him realize his mistake she sat in the hawan kund of the yagna and burned her and she died, though shiva made daksha realize his mistake later.
She was then again born to shailraj Himalaya and was named parvati and got married to shiva. She is worshipped by remembering her in the navratri period once in chaitra month and once in the period of ashwin month both falls in April and October respectively.