In India, Navaratri is celebrated four times a year. They are Ashada Navaratri, the Sharad Navaratri, the Maha Navaratri and the Vasantha Navaratri. Of these, the Sharad Navaratri of the month of Ashwiyuja / Puratashi and the Vasantha Navaratri of the Vasantha kala are very important. The Agni purana states that Ashwiyuja and Chaitra (Puratashi and Panguni (in Tamil months)) are like the two jaws of Lord Yama. If one wants to escape the mouth of Yama, then one should celebrate Navaratri on these two occasions.
A similar analogy is presented in the Devi Bhagavatam. Devi Bhagavatam also sets forth in detail about how one should observe fasts, and how one should meditate/work on these days. It is a long held tradition to read the Devi-Bhagavatam or the Devi Mahatmyam (Durga Saptasati, 700 verses on Durga) during this period. Devi Bhagavatam notes that Rama meditated and fasted for nine days after Sita was kidnapped by Ravana. There are numerous such incidents on how people’s wishes were fulfilled. A lot more details are available in Devi Bhagavatam.